Question

Find the equation of a line that has a slope of 2 and passes through the point.
point (-7, 5)

Answer 1

`\large\boxed{y-5=2(x+7)\leftarrow\text{point-slope form}}\\\boxed{y=2x+19\leftarrow\text{slope-intercept form}}`

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

m - slope

(x₁, y₁) - point

We have the slope m = 2 and the point (-7, 5) → x₁ = -7, y₁ = 5.

Substitute:

`y-5=2(x-(-7))\\\\y-5=2(x+7)`

Convert to the slope-intercept form (y = mx + b):

`y-5=2(x+7)` use distributive property

`y-5=2x+14` add 5 to both sides

`y=2x+19`