Question

A straight line has slope 4 and goes through the points (0,– 2) and (a, 26).Write the equation of the line in the form y=mx+b.

Answer 1

Solve for the y-intercept

`\begin{gathered} \text{Given the points} \\ (0,-2)\text{ and }(a,26)\text{ and slope of }m\text{ we can solve directly for the equation} \\ \\ \text{Use point }(0,-2)\text{ in the equation and }m=4 \\ \\ y=mx+b \\ \text{Substitute} \\ x=0,y=-2,m=4 \\ \\ y=mx+b \\ -2=(4)(0)+b \\ -2=b \\ \\ b=-2 \end{gathered}`

Now that we have the y-intercept, putting it together with m = 4, and b = -2.

`\begin{gathered} \text{The equation of the line is} \\ y=4x-2 \end{gathered}`