Question

Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.Slope: 2, ordered pair: (-2,2)

Answer 1

The slope-intercept form of a line is defined as

`\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}`

Given a slope m = 2, and a point (x,y) of (-2,2) substitute the following values to the definition of a slope intercept form, and we get

`\begin{gathered} y=mx+b \\ m=2 \\ x=-2 \\ y=2 \\ \\ \text{Substitute} \\ y=mx+b \\ 2=(2)(-2)+b \\ 2=-4+b \\ 2+4=b \\ b=6 \end{gathered}`

Now that we have the y-intercept form, put it all together along with the slope, and the equation of the line is

`y=2x+6`