Question

Use point-slopesto write the eq. in slope-int form. (1,5) and (5, 13)

Answer 1

Answer:

y=2x+3.

Explanation:

The point-slope form of the equation of a line is:

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{where:} \\ \text{Slope, m=}=\frac{y_2-y_1}{x_2-x_1} \\ \implies y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}$

Substituting the points (x1,y1)=(1,5) and (x2,y2)=(5,13):

$\begin{gathered} y-5=\frac{13-5}{5-1}(x-1) \\ y-5=\frac{8}{4}(x-1) \\ y-5=2(x-1) \\ y-5=2x-2 \\ y-5=2x-2+5 \\ y=2x+3 \end{gathered}$

The equation in slope-intercept form is y=2x+3.