Chapter SH, Problem 4.7EP

To determine

To write in slope intercept form for the line that passes through the point $(-2,5)$ and $(-4,13)$ .

Answer to Problem 4.7EP

The slope intercept form is $y=-4x-3$

Explanation of Solution

Given information:

The line that passes through the pairs of point $(-2,5)$ and $(-4,13)$ .

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 $(-2,5)$ and $(-4,13)$ into slope intercept form

  $x_1=-2$

  $y_1=5$

  $x_2=-4$

  $y_2=13$

Using slope formula to calculate slope of pair of points

  $m=\frac{13-5}{(-4)-(-2)}$

So,

  $m=\frac{8}{-2}$

On solving,

Slope, $m=-4$

Using slope intercept form formula to calculate Y-intercept

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

Point $\text{(-2 , 5) }$ taken to calculate Y-intercept

  $5=-4(-2)+b$

So,

  $5-8=b$

On solving,

  $b=-3$

Substituting value of b and m in the slope intercept form

  $y=(-4)x-3$

So,

  $y=-4x-3$

Hence, the slope intercept form is $y=-4x-3$