Chapter SH, Problem 4.5EP

To determine

To write in slope intercept form for the line that passes through the point $(-3,1)$ and $(2,7).$

Answer to Problem 4.5EP

The slope intercept form is $y=(\frac{6}{5})x+\frac{9}{5}$

Explanation of Solution

Given information:

The line that passes through the pairs of point $(-3,1)$ and $(2,7).$

Formula used:

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

Slope intercept form $y=mx+b$

Calculation:

Slope intercept form: The graph of the equation $y=mx+b$ (where m and b are real numbers) is a line with slope, m, and y-intercept, b.This form of the equation of a line is called the slope-intercept form.

Formation of point $(-3,1)$ and $(2,7).$ into slope intercept form

  $x_1=-3$

  $y_1=1$

  $x_2=2$

  $y_2=7$

Using slope formula to calculate slope of pair of points

  $m=\frac{7-1}{2-(-3)}$

On solving,

Slope, $m=\frac{6}{5}$

Using slope intercept form formula to calculate Y-intercept

Use any one of the given points to calculate Y-intercept

Point $(-3,1)$ taken to calculate Y-intercept

  $y=mx+b$

  $-3=\frac{6}{5}(-4)+b$

On solving,

  $b=\frac{9}{5}$

Substituting value of b and m in the slope intercept form

So,

  $y=(\frac{6}{5})x+\frac{9}{5}$

Hence, the slope intercept form is $y=(\frac{6}{5})x+\frac{9}{5}$