Chapter SH, Problem 4.3EP

To determine

To write in slope intercept form for the line that passes through the point $(0,-1)$ and $(1,1)$ .

Answer to Problem 4.3EP

The slope intercept form is $y=2x-1$

Explanation of Solution

Given information:

The line that passes through the pairs of point $(0,-1)$ and $(1,1)$ .

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 $(0,-1)$ and $(1,1)$ into slope intercept form

  $x_1=0$

  $y_1=-1$

  $x_2=1$

  $y_2=1$

Using slope formula to calculate slope of pair of points

  $m=\frac{1-(-1)}{1-0}$

On solving,

Slope, $m=2$

Using slope intercept form formula to calculate Y-intercept

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

Point $(0,-1)$ taken to calculate Y-intercept

  $y=mx+b$

  $-1=2(0)+b$

On solving,

  $b=-1$

Substituting value of b and m in the slope intercept form

  $y=mx+b$

  $y=2x-1$

Hence, the slope intercept form is $y=2x-1$