Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Answer:

$y = -\frac{2}{5} x-6$

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula $m =\frac{y_2-y_1}{x_2-x_1}$. Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):

$m = \frac{(-6)-(-4)}{(0)-(-5)} \\m = \frac{-6+4}{0+5} \\m = \frac{-2}{5}$  

So, the slope of the line is $-\frac{2}{5}$.

2) Next, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the $m$, $x_1$ and $y_1$ into the formula.

Since $m$ represents the slope, substitute $-\frac{2}{5}$  in its place. Since $x_1$ and $y_1$ represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form:

$y-(-6) = -\frac{2}{5} (x-(0))\\y + 6 = -\frac{2}{5} x\\y = -\frac{2}{5} x-6$