How to graph a function

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SSAT Upper Level Quantitative › How to graph a function

Questions 1 - 2

Axes

Refer to the above diagram. If the red line passes through the point $\left ( N, 4\right )$ , what is the value of ?

$N = -4\frac{2}{3}$

$N= -1\frac{1}{3}$

$N = -7\frac{1}{3}$

$N = -3\frac{1}{3}$

Explanation

One way to answer this is to first find the equation of the line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$ :

$m = \frac{18-0}{0-(-6)} = \frac{18}{6} = 3$

The line has slope 3 and -intercept , so we can substitute in the slope-intercept form:

Now substitute 4 for and for and solve for :

$N = -\frac{14}{3}= -4\frac{2}{3}$

Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. Give the equation of that line in slope-intercept form.

$y = - \frac{1}{2}x + 8$

$y = \frac{1}{2}x + 8$

$y = - \frac{1}{2}x + 4$

$y = \frac{1}{2}x + 4$

$y = \frac{1}{2}x - 4$

Explanation

First, we need to find the slope of the above line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be $m = -\frac{1}{2}$ . Since we want this line to have the same -intercept as the first line, which is the point , we can substitute $m = -\frac{1}{2}$ and in the slope-intercept form:

$y = - \frac{1}{2}x + 8$

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