Chapter SH, Problem 4.4EP

To determine

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

Answer to Problem 4.4EP

The slope intercept form is $y=x$ .

Explanation of Solution

Given information:

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

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

  $x_1=-4$

  $y_1=-4$

  $x_2=2$

  $y_2=2$

Using slope formula to calculate slope of pair of points

  $m=\frac{2-(-4)}{2-(-4)}$

On solving,

Slope

  $m=1$

Using slope intercept form formula to calculate Y-intercept

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

Point $(-4,-4)$ taken to calculate Y-intercept

  $y=mx+b$

  $-4=1(-4)+b$

So,

  $-4+4=b$

On solving,

  $b=0$

Substituting value of b and m in the slope intercept form

  $y=(1)x+0$

So,

  $y=x$

Hence, the slope intercept form is $y=x$