$\text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. }$
A) $y = - \frac { 5 } { 6 } x - 8$
B) $y = \frac { 5 } { 6 } x - 8$
C) $y = \frac { 5 } { 6 } x + 8$
D) $y = - \frac { 5 } { 6 } x + 8$
E) $y = - \frac { 5 } { 6 } x$

Question

$\text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. }$ 
A) $y = - \frac { 5 } { 6 } x - 8$
B) $y = \frac { 5 } { 6 } x - 8$
C) $y = \frac { 5 } { 6 } x + 8$
D) $y = - \frac { 5 } { 6 } x + 8$
E) $y = - \frac { 5 } { 6 } x$

Quizplus · Accepted Answer

We will use the point-slope form of a linear equation: 
$y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is any point on the line.

First, let's find the slope of the line:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
$$m = \frac{23 - (-7)}{-18 - 18}$$
$$m = -\frac{5}{6}$$

Now, we can use either point as our $(x_1,y_1)$. Let's use $(18,-7)$:

$$y - (-7) = -\frac{5}{6}(x - 18)$$
$$y + 7 = -\frac{5}{6}x + \frac{5}{6}(18)$$
$$y + 7 = -\frac{5}{6}x + 15$$
$$y = -\frac{5}{6}x + 8$$

So the equation of the line that passes through the two points is $y = -\frac{5}{6}x + 8$, which is choice (D).

Find an equation of the line that passes through the points (18,−7) and (−18,23). \text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. } Find an equation of the line that passes through the points (18,−7) and (−18,23).

$\text { Find an equation of the line that passes through the points } ( 18 , - 7 ) \text { and } ( - 18,23 ) \text {. }$