Question

what is the equation of the line that passes through the points (-5,0) and (-2,0)?
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what is the equation of the line that passes through the points (15,2) and (12,1)? write your answer in slope - intercept form.
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Explanation:

Step1: Calculate slope for first line

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $(-5,0)$ and $(-2,0)$, $x_1=-5,y_1 = 0,x_2=-2,y_2 = 0$. Then $m=\frac{0 - 0}{-2-(-5)}=\frac{0}{3}=0$.
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(-5,0)$ and $m = 0$, we get $y-0=0(x + 5)$, so the equation is $y = 0$.

Step2: Calculate slope for second line

For points $(15,2)$ and $(12,1)$, $x_1 = 15,y_1=2,x_2=12,y_2 = 1$. Then $m=\frac{1 - 2}{12-15}=\frac{-1}{-3}=\frac{1}{3}$.

Step3: Find y - intercept for second line

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(15,2)$ and $m=\frac{1}{3}$, we have $y - 2=\frac{1}{3}(x - 15)$.
Expand: $y-2=\frac{1}{3}x-5$.
Add 2 to both sides to get slope - intercept form $y=\frac{1}{3}x-3$.

Answer:

$y = 0$
$y=\frac{1}{3}x-3$