PSAT Math : How to find x or y intercept

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Find X Or Y Intercept

Determine the y-intercept of the following line:

\dpi{100} \small 3x+6y=9\(\displaystyle \dpi{100} \small 3x+6y=9\)

Possible Answers:

\dpi{100} \small 6\(\displaystyle \dpi{100} \small 6\)

\dpi{100} \small 1.5\(\displaystyle \dpi{100} \small 1.5\)

\dpi{100} \small \frac{1}{3}\(\displaystyle \dpi{100} \small \frac{1}{3}\)

\dpi{100} \small 3\(\displaystyle \dpi{100} \small 3\)

\dpi{100} \small 9\(\displaystyle \dpi{100} \small 9\)

Correct answer:

\dpi{100} \small 1.5\(\displaystyle \dpi{100} \small 1.5\)

Explanation:

The y-intercept occurs when \dpi{100} \small x=0\(\displaystyle \dpi{100} \small x=0\)

\dpi{100} \small 3x+6y=9\(\displaystyle \dpi{100} \small 3x+6y=9\)

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

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

\dpi{100} \small y = \frac{9}{6}=1.5\(\displaystyle \dpi{100} \small y = \frac{9}{6}=1.5\)

Example Question #2 : How To Find X Or Y Intercept

At what point does the graph 3y-2x=31\(\displaystyle 3y-2x=31\) cross the \(\displaystyle y\)-axis?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Example Question #11 : How To Find X Or Y Intercept

Find the x-intercepts of  25x^{2}+4y^{2} = 9\(\displaystyle 25x^{2}+4y^{2} = 9\).

Possible Answers:

\pm 5\(\displaystyle \pm 5\)

2\(\displaystyle 2\)

5\(\displaystyle 5\)

\pm \frac{3}{5}\(\displaystyle \pm \frac{3}{5}\)

\frac{3}{5}\(\displaystyle \frac{3}{5}\)

Correct answer:

\pm \frac{3}{5}\(\displaystyle \pm \frac{3}{5}\)

Explanation:

To find the x-intercepts, plug y=0\(\displaystyle y=0\) into the equation and solve for x\(\displaystyle x\).

25x^{2} + 4\cdot 0^{2} = 9\(\displaystyle 25x^{2} + 4\cdot 0^{2} = 9\)

25x^{2} = 9\(\displaystyle 25x^{2} = 9\)

x^{2} = \frac{9}{25}\(\displaystyle x^{2} = \frac{9}{25}\)

x = \pm \frac{3}{5}\(\displaystyle x = \pm \frac{3}{5}\)

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

Example Question #11 : How To Find X Or Y Intercept

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

Possible Answers:

\(\displaystyle 6\)

\(\displaystyle 4\)

\(\displaystyle 2\)

\(\displaystyle -2\)

\(\displaystyle -1\)

Correct answer:

\(\displaystyle 2\)

Explanation:

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

Example Question #11 : How To Find X Or Y Intercept

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

\(\displaystyle y=x^2+12x+27\)

Possible Answers:

\(\displaystyle x=3,9\)

\(\displaystyle x=3,-9\)

\(\displaystyle x=27,1\)

\(\displaystyle x=-3,9\)

\(\displaystyle x=-3,-9\)

Correct answer:

\(\displaystyle x=-3,-9\)

Explanation:

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

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

 

Therefore our \(\displaystyle x\)-intercepts are \(\displaystyle -3\) and \(\displaystyle -9\).

Example Question #11 : How To Find X Or Y Intercept

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

Possible Answers:

\(\displaystyle y=\frac{1}{4}x-7\)

\(\displaystyle y=4x-7\)

\(\displaystyle y = -4x + 5\)

\(\displaystyle y = 4x + 7\)

\(\displaystyle y=-\frac{1}{4}x+11\)

Correct answer:

\(\displaystyle y = -4x + 5\)

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.

Example Question #12 : How To Find X Or Y Intercept

Where does the line given by y=3(x-4)-9\(\displaystyle y=3(x-4)-9\) intercept the \(\displaystyle x\)-axis?

Possible Answers:

\(\displaystyle -7\)

\(\displaystyle 7\)

\(\displaystyle 3\)

\(\displaystyle \frac{4}{3}\)

Correct answer:

\(\displaystyle 7\)

Explanation:

First, put in slope-intercept form. 

\(\displaystyle y = 3x-12-9\)

y=3x-21\(\displaystyle y=3x-21\)

To find the \(\displaystyle x\)-intercept, set \(\displaystyle y=0\) and solve for \(\displaystyle x\).

\(\displaystyle 0=3x-21\)

\(\displaystyle 3x=21\)

\(\displaystyle x=7\)

Example Question #13 : How To Find X Or Y Intercept

Find the y-intercept of \(\displaystyle y = 3x^2 +2x + 7\).

Possible Answers:

14

7

5

3

12

Correct answer:

7

Explanation:

To find the y-intercept, set x equal to zero and solve for y.

This gives y = 3(0)2 + 2(0) +7 = 7.

Example Question #12 : How To Find X Or Y Intercept

The slope of a line is m=\frac{4}{3}\(\displaystyle m=\frac{4}{3}\). The line passes through (2,7)\(\displaystyle (2,7)\). What is the x-intercept?

Possible Answers:

(4\frac{1}{3},0)\(\displaystyle (4\frac{1}{3},0)\)

(0,9\frac{2}{3})\(\displaystyle (0,9\frac{2}{3})\)

None of the available answers

(0,4.3)\(\displaystyle (0,4.3)\)

\(\displaystyle \left ( -3\frac{1}{4},0\right )\)

Correct answer:

\(\displaystyle \left ( -3\frac{1}{4},0\right )\)

Explanation:

The equation for a line is:

y=mx+b\(\displaystyle y=mx+b\), or in this case

y=\frac{4}{3}x+b\(\displaystyle y=\frac{4}{3}x+b\)

We can solve for b\(\displaystyle b\) by plugging in the values given

7=\frac{4}{3}\times 2+b\(\displaystyle 7=\frac{4}{3}\times 2+b\)

7=2\frac{2}{3}+b\(\displaystyle 7=2\frac{2}{3}+b\)

b=7-2\frac{2}{3}=4\frac{1}{3}\(\displaystyle b=7-2\frac{2}{3}=4\frac{1}{3}\)

Our line is now

y=\frac{4}{3}x+4\frac{1}{3}\(\displaystyle y=\frac{4}{3}x+4\frac{1}{3}\)

Our x-intercept occurs when \dpi{100} y=0\(\displaystyle \dpi{100} y=0\), so plugging in and solving for \dpi{100} x\(\displaystyle \dpi{100} x\):

\dpi{100} 0=\frac{4}{3}x+4\frac{1}{3}\(\displaystyle \dpi{100} 0=\frac{4}{3}x+4\frac{1}{3}\)

\dpi{100} -\frac{13}{3}=\frac{4}{3}x\(\displaystyle \dpi{100} -\frac{13}{3}=\frac{4}{3}x\)

\dpi{100} x=-\frac{13}{4}\(\displaystyle \dpi{100} x=-\frac{13}{4}\)

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