Explanation
We have the given slope which is m=-7 and the given coordinate point.
[tex]y = mx + b[/tex]
Substitute m = -7 in the equation.
[tex]y = - 7x + b[/tex]
After we substitute the slope, we substitute the value of coordinate point.
[tex]0 = - 7(4) + b \\ 0 = - 28 + b \\ 28 = b[/tex]
Substitute the value of b in the equation and rewrite the new equation.
[tex]y = - 7x + 28[/tex]
We can use the Point-Slope form to find the slope-intercept form with given slope and coordinate point.
[tex]y - y_1 = m(x - x_1)[/tex]
where y1 and x1 both are the coordinate point.
Substitute m = -7, y1 = 0 and x1 = 4 in the point-slope form.
[tex]y - 0 = - 7(x - 4)[/tex]
Simplify the equation and convert in the slope-intercept form
[tex]y = - 7(x - 4) \\ y = - 7x + 28[/tex]
Answer
[tex] \large \boxed {y = - 7x + 28}[/tex]
