Write an equation of the line passing through (-5 ,4 ) and having slope - 7

y = - 7x - 31

the equation of a line in slope-intercept form is

y = mx + c (m is the slope and c the y-intercept)

here m = - 7

y = - 7x + c ← is the partial equation

to find c substitute ( - 5, 4) into the partial equation

4 = 35 + c ⇒ c = 4 - 35 = - 31

y = - 7x - 31 ← equation in slope-intercept form

So the equation of a line is y=mx+b

Now substitute what you know

4 = - 5 * - 7 + b

4 = 35+b

b=-31

So the equation is:

y = - 7x - 31