Answer:
[tex]\large\boxed{y-5=2(x+7)\leftarrow\text{point-slope form}}\\\boxed{y=2x+19\leftarrow\text{slope-intercept form}}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the slope m = 2 and the point (-7, 5) → x₁ = -7, y₁ = 5.
Substitute:
[tex]y-5=2(x-(-7))\\\\y-5=2(x+7)[/tex]
Convert to the slope-intercept form (y = mx + b):
[tex]y-5=2(x+7)[/tex] use distributive property
[tex]y-5=2x+14[/tex] add 5 to both sides
[tex]y=2x+19[/tex]
