Question

Find the equation of the line using the given information and the point-slope form. Express the equation in slope-intercept form slope = 2Point = (5,7)

Answer 1

Given the point (5, 7) and the slope 2, using the point-slope form we have the equation of the line:

`y-y_0=m(x-x_0)`

Where m is the slope and x₀ and y₀ are the coordinates of the given point. From this problem, we identify m = 2, x₀ = 5, and y₀ = 7. Then:

`y-7=2(x-5)\ldots(1)`

The slope-intercept form is given by:

`y=m\cdot x+b`

Where m is the slope and b is the y-intercept. Using equation (1):

`\begin{gathered} y=2x-10+7 \\ y=2x-3 \end{gathered}`