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PSAT Math : Arcs and Intercept

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Example Questions

Example Question #5 : How To Find X Or Y Intercept

A line has the equation: 2x+4y=8.

What is the x-intercept?

Possible Answers:

-8

-4

Correct answer:

Explanation:

To find the x-intercept, rearrange the equation 2x+4y=8 so that x is isolated:

2x=-4y+8

x=-2y+4

Using the point-slope formula, we see that the x-intercept is 4.

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Example Question #161 : Geometry

Given the line 4x + 3y = 12 , what is the sum of the -intercept and the -intercept?

Possible Answers:

Correct answer:

Explanation:

Intercepts occur when a line crosses the -axis or the -axis. When the line crosses the -axis, then y = 0 and x = 3 . When the line crosses the -axis, then x = 0 and y = 4 . The intercept points are (0, 4) and (3, 0 ) . So the -intercept is and the intercept is and the sum is .

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Example Question #6 : How To Find X Or Y Intercept

What is the y intercept of the following function of x?

y = 3x

Possible Answers:

–3

–1

Correct answer:

Explanation:

The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.

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Example Question #3 : How To Find X Or Y Intercept

What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?

Possible Answers:

(–3.5, 0)

(0, –0.7)

(0.7, 0)

(–0.7, 0)

(3.5, 0)

Correct answer:

(–0.7, 0)

Explanation:

To solve this, first find the equation of our line. The form of the question gives it to us very directly. We can use the slope-intercept form (y = mx + b).

y = 5x + 3.5

The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis.

0 = 5x + 3.5; –3.5 = 5x; x = –3.5 / 5 or –0.7. The point will be (–0.7, 0)

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Example Question #4 : How To Find X Or Y Intercept

Determine the y-intercept of the following line:

$\dpi{100} \small 3x+6y=9$

Possible Answers:

$\dpi{100} \small 9$

$\dpi{100} \small 6$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small 1.5$

$\dpi{100} \small 3$

Correct answer:

$\dpi{100} \small 1.5$

Explanation:

The y-intercept occurs when $\dpi{100} \small x=0$

$\dpi{100} \small 3x+6y=9$

$\dpi{100} \small 3(0)+6y=9$

$\dpi{100} \small 0+6y=9$

$\dpi{100} \small y = \frac{9}{6}=1.5$

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Example Question #161 : Psat Mathematics

At what point does the graph $3y-2x=31$ cross the -axis?

Possible Answers:

$\left ( 0,\frac{31}{3} \right )$

$\left ( 0,\frac{2}{3} \right )$

$\left ( 0,-\frac{2}{3} \right )$

$\left ( 0,\frac{3}{31} \right )$

$\left ( 0,\frac{3}{2} \right )$

Correct answer:

$\left ( 0,\frac{31}{3} \right )$

Explanation:

The graph crosses the -axis where $x=0$ . So plugging in and solving yields $\frac{31}{3}$ .

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Example Question #162 : Geometry

Find the x-intercepts of $25x^{2}+4y^{2} = 9$ .

Possible Answers:

$\pm 5$

$5$

$\frac{3}{5}$

$2$

$\pm \frac{3}{5}$

Correct answer:

$\pm \frac{3}{5}$

Explanation:

To find the x-intercepts, plug $y=0$ into the equation and solve for $x$ .

$25x^{2} + 4\cdot 0^{2} = 9$

$25x^{2} = 9$

$x^{2} = \frac{9}{25}$

$x = \pm \frac{3}{5}$

Don't forget that there are two solutions, both negative and positive!

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Example Question #163 : Geometry

A line with the exquation $y=x^2+3x+c$ passes through the point (-4,6) . What is the -intercept?

Possible Answers:

Correct answer:

Explanation:

By plugging in the coordinate, we can figure out that c=2 . The -Intercept is when x=0 , plugging in 0 for gives us y=2 .

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Example Question #21 : Arcs And Intercept

What are the -intercept(s) of the following line:

y=x^2+12x+27

Possible Answers:

x=3,-9

x=-3,9

x=27,1

x=3,9

x=-3,-9

Correct answer:

x=-3,-9

Explanation:

We can factor y=x^2+12x+27 and set equal to zero to determine the -intercepts.

y=(x+3)(x+9) satisfies this equation.

Therefore our -intercepts are and .

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Example Question #22 : Arcs And Intercept

Which of the following lines does not intersect the line 4x + y = 7 ?

Possible Answers:

y=4x-7

$y=\frac{1}{4}x-7$

$y=-\frac{1}{4}x+11$

y = -4x + 5

y = 4x + 7

Correct answer:

y = -4x + 5

Explanation:

Parallel lines never intersect, so you are looking for a line that has the same slope as the one given. The slope of the given line is –4, and the slope of the line in y = –4x + 5 is –4 as well. Since these two lines have equal slopes, they will run parallel and can never intersect.

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PSAT Math : Arcs and Intercept

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #5 : How To Find X Or Y Intercept

Example Question #161 : Geometry

Example Question #6 : How To Find X Or Y Intercept

Example Question #3 : How To Find X Or Y Intercept

Example Question #4 : How To Find X Or Y Intercept

Example Question #161 : Psat Mathematics

Example Question #162 : Geometry

Example Question #163 : Geometry

Example Question #21 : Arcs And Intercept

Example Question #22 : Arcs And Intercept

All PSAT Math Resources

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