📝 Finding x and y intercepts from graph (15 MCQs)

📖 From Digital SAT Algebra • 4. Graphs • 15 questions available

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What is Finding x and y intercepts from graph?

Definition:
Finding x and y intercepts from a graph involves identifying the points where the line or curve crosses the x-axis (y = 0) and the y-axis (x = 0); these intercepts are read directly from the graph by noting the coordinates where the graph intersects the axes, providing important information about the function or equation, and they are used to write equations and interpret graphs.

Working:
To find the x-intercept from a graph, locate the point where the graph crosses the x-axis; the y-coordinate is 0, and the x-coordinate is the intercept value; to find the y-intercept, locate where the graph crosses the y-axis; the x-coordinate is 0, and the y-coordinate is the intercept value; these points are often easy to spot, and they can be used to determine the equation of the line in slope-intercept form or standard form, by using the intercepts to find slope and then writing the equation.

Example:
A simple example is a line that crosses the x-axis at x = -3 (so x-intercept is -3, point (-3, 0)) and crosses the y-axis at y = 2 (so y-intercept is 2, point (0, 2)); these intercepts can be read directly from the graph, illustrating how intercepts are extracted visually.

Reason:
Finding intercepts from a graph is a core skill in algebra and graphing, as they provide essential information about the equation, and they are used in many applications, including physics (initial positions) and economics (break-even points), making this a practical skill.

Easy

Medium

Hard

📝 All Finding x and y intercepts from graph MCQs

Q1. A graph crosses the x-axis at $x=-4$ and the y-axis at $y=6$ . Which ordered pair correctly represents the x-intercept and why?

(-4,0)

, because every x-intercept has

y=0

✅

(0,6)

, because every x-intercept has

x=0

(-4,6)

, because both coordinates are read from the graph

(6,-4)

, because the coordinates must be reversed

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: An x-intercept is located where a graph meets the x-axis, whose $y$ -coordinate is always zero. Therefore, the crossing at $x=-4$ is represented by $(-4,0)$ , while $(0,6)$ is the y-intercept.

Q2. A line intersects the y-axis at $(0,-7)$ and the x-axis at $(5,0)$ . Which statement correctly distinguishes the two intercepts?

A.The x-intercept is

(0,-7)

because it appears first

B.The y-intercept is

(5,0)

because its x-coordinate is positive

C.The x-intercept is

(5,0)

and the y-intercept is

(0,-7)

✅

D.Both points are x-intercepts because both lie on the same line

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: The defining feature of an x-intercept is a zero $y$ -coordinate, while a y-intercept has a zero $x$ -coordinate. Thus $(5,0)$ is the x-intercept and $(0,-7)$ is the y-intercept.

Q3. Two students identify an x-intercept. Student A says it is $(0,8)$ , while Student B says it is $(8,0)$ . Which reasoning is mathematically correct?

A.Student A, because the y-coordinate identifies the intercept

B.Student B, because points on the x-axis have

y=0

✅

C.Student A, because x-intercepts must have

x=0

D.Both students, because either coordinate can be zero

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Points on the x-axis always have $y=0$ . Therefore, if the graph crosses the x-axis at $x=8$ , the correct coordinate is $(8,0)$ . A zero x-coordinate instead identifies a point on the y-axis.

Q4. A graph has a point on the x-axis at $x=-3$ and another point on the y-axis at $y=4$ . Which pair gives the intercepts in the correct order?

A.x-intercept

(0,-3)

, y-intercept

(4,0)

B.x-intercept

(-3,0)

, y-intercept

(0,4)

✅

C.x-intercept

(3,0)

, y-intercept

(0,-4)

D.x-intercept

(-3,4)

, y-intercept

(0,0)

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The x-intercept must lie on the horizontal axis, so its y-coordinate is zero, giving $(-3,0)$ . The y-intercept lies on the vertical axis, so its x-coordinate is zero, giving $(0,4)$ .

Q5. A graph crosses the x-axis at $(-6,0)$ and the y-axis at $(0,2)$ . A student claims the y-intercept is $(2,0)$ . What mistake did the student make?

A.They changed the sign of the x-coordinate

B.They treated the intercept value as an x-coordinate instead of a y-coordinate ✅

C.They confused the x-axis with the origin

D.They should have written

(-6,2)

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The student correctly noticed the value $2$ but placed it in the wrong coordinate position. A y-intercept always has $x=0$ , so the correct point is $(0,2)$ , not $(2,0)$ .

Q6. A line intersects the x-axis at $x=9$ and the y-axis at $y=-3$ . Which conclusion can be made without knowing the equation of the line?

A.The intercepts are

(9,0)

and

(0,-3)

✅

B.The intercepts are

(0,9)

and

(-3,0)

C.The line must have positive slope

D.The line must have negative slope

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The graph itself provides enough information to identify the intercepts because their axis locations determine one coordinate as zero. The x-intercept is $(9,0)$ , and the y-intercept is $(0,-3)$ .

Q7. A business graph shows revenue becoming zero when production reaches $120$ units. The same graph shows revenue of $-500$ when production is zero. Which interpretation correctly identifies the intercepts?

A.x-intercept

(0,120)

, y-intercept

(-500,0)

B.x-intercept

(120,0)

, y-intercept

(0,-500)

✅

C.Both intercepts have positive coordinates

D.x-intercept

(-500,0)

, y-intercept

(120,0)

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Production is represented by the horizontal coordinate and revenue by the vertical coordinate. Revenue becomes zero at $120$ units, giving the x-intercept $(120,0)$ . At zero production, revenue is $-500$ , giving $(0,-500)$ .

Q8. A graph of temperature versus time crosses the horizontal axis at $t=6$ hours and the vertical axis at $20^\circ$ . What do the two intercepts mean in this context?

A.The x-intercept means temperature is

6^\circ

, while the y-intercept means time is 20 hours

B.The x-intercept means temperature is zero at 6 hours, while the y-intercept gives the initial temperature ✅

C.Both intercepts represent times when temperature is zero

D.The x-intercept gives the initial temperature, while the y-intercept gives when temperature becomes zero

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The horizontal coordinate represents time and the vertical coordinate represents temperature. Therefore, the x-intercept $(6,0)$ means the temperature reaches zero after 6 hours, while the y-intercept $(0,20)$ represents the initial temperature.

Q9. A student reads a graph and records the intercepts as $(0,-5)$ and $(-2,0)$ , but labels the first as the x-intercept and the second as the y-intercept. How should the labels be corrected?

A.Keep both labels unchanged

B.Swap the labels of the two points ✅

C.Change both coordinates to positive values

D.Change

(-2,0)

(0,-2)

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The point $(0,-5)$ lies on the y-axis because its x-coordinate is zero, so it is the y-intercept. The point $(-2,0)$ lies on the x-axis because its y-coordinate is zero, so it is the x-intercept.

Q10. A graph crosses the x-axis at $4$ , then later crosses the y-axis at $-8$ . Which pair of coordinates should be entered into a data table specifically labeled x-intercept and y-intercept?

A.x-intercept

(0,4)

, y-intercept

(-8,0)

B.x-intercept

(4,0)

, y-intercept

(0,-8)

✅

C.x-intercept

(4,-8)

, y-intercept

(0,0)

D.x-intercept

(-4,0)

, y-intercept

(0,8)

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The axis on which an intercept lies determines which coordinate becomes zero. Since the graph crosses the x-axis at $4$ , its x-intercept is $(4,0)$ . Crossing the y-axis at $-8$ gives $(0,-8)$ .

Q11. A graph appears to cross the x-axis near $x=3.9$ and the y-axis near $y=7.1$ . If the graph is drawn accurately but only integer coordinates are required, which values are most reasonable to report?

A.x-intercept

(4,0)

, y-intercept

(0,7)

✅

B.x-intercept

(0,4)

, y-intercept

(7,0)

C.x-intercept

(3,0)

, y-intercept

(0,8)

D.x-intercept

(3.9,7.1)

, y-intercept

(3.9,7.1)

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The graph indicates approximate intercept locations of $3.9$ and $7.1$ . When integer coordinates are explicitly requested, rounding gives $4$ and $7$ . The corresponding points are therefore $(4,0)$ and $(0,7)$ .

Q12. A graph passes through $(-5,0)$ , $(0,3)$ , and $(2,4)$ . Which statement best verifies the intercepts using the axis definitions?

A.Only

(-5,0)

is an intercept because it has a negative coordinate

(-5,0)

is the x-intercept and

(0,3)

is the y-intercept ✅

(0,3)

is the x-intercept because its first coordinate is zero

D.All three points are intercepts because they lie on the same line

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: An intercept must lie directly on one of the coordinate axes. The point $(-5,0)$ lies on the x-axis, while $(0,3)$ lies on the y-axis. The point $(2,4)$ lies on neither axis.

Q13. A line crosses the x-axis at $x=12$ and the y-axis at $y=18$ . A student finds the intercepts by first locating where each coordinate becomes zero. Which result confirms the student's method?

A.The intercepts are

(12,0)

and

(0,18)

✅

B.The intercepts are

(0,12)

and

(18,0)

C.The intercepts are

(12,18)

and

(0,0)

D.The intercepts are

(-12,0)

and

(0,-18)

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Setting the y-coordinate to zero identifies the x-intercept, producing $(12,0)$ . Setting the x-coordinate to zero identifies the y-intercept, producing $(0,18)$ . This method directly matches the geometric meaning of each intercept.

Q14. A graph intersects the x-axis at $(-a,0)$ and the y-axis at $(0,a)$ , where $a>0$ . Which statement is necessarily true about these intercepts?

A.Both intercepts are on the positive side of their axes

B.Both intercepts are on the negative side of their axes

C.The x-intercept is negative and the y-intercept is positive ✅

D.The x-intercept is positive and the y-intercept is negative

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Because $a>0$ , the x-coordinate $-a$ is negative, placing the x-intercept on the negative x-axis. The y-coordinate $a$ is positive, placing the y-intercept on the positive y-axis. Thus option C is necessary.

Q15. A line has x-intercept $(6,0)$ and y-intercept $(0,-9)$ . Another line has x-intercept $(3,0)$ and y-intercept $(0,-9)$ . Which conclusion is valid when comparing the two graphs?

A.Both lines have identical intercepts

B.The second line reaches the x-axis closer to the origin ✅

C.The first line must have a smaller magnitude slope

D.Both lines cross the x-axis at the same location

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The x-intercept measures the horizontal distance from the origin to the point where the graph reaches the x-axis. The second line has x-intercept $3$ , compared with $6$ for the first, so it reaches the x-axis closer to the origin.

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