Question

A line has a slope of – 4 and passes through the point (2, – 15). Write its equation in slope-intercept form.

Answer 1

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-15})\hspace{10em} \stackrel{slope}{m} ~=~ -4 \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-15)}=\stackrel{m}{-4}(x-\stackrel{x_1}{2}) \implies y +15 = -4 ( x -2) \\\\\\ y+15=-4x+8\implies {\Large \begin{array}{llll} y=-4x-7 \end{array}}`

Answer 2

Slope-intercept form: y = -4x - 7

Explanation:

Finding b (the y-intercept):

The general equation of the slope-intercept form is given by:

y = mx + b, where

• m is the slope,
• and b is the y-intercept.

Since we already know the slope is -4 and the line passes through (2, -15), we can solve for b (the y-intercept) by plugging in -4 for m and (2, -15) for (x, y) in the slope-intercept form:

-15 = -4(2) + b

(-15 = -8 + b) + 8

-7 = b

Thus, the y-intercept is -7.

Writing the equation of the line in slope-intercept form:

Therefore, y = -4x - 7 is the equation of the line in slope-intercept form whose slope is -4 and that passes through the point (2, -15).