Chapter SH, Problem 4.8EP

To determine

To write in slope intercept form for the line that passes through the point $\text{(3 , 7)}$ and $\text{(9 , 19)}$ .

Answer to Problem 4.8EP

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

Explanation of Solution

Given information:

The line that passes through the pairs of point $\text{(3 , 7)}$ and $\text{(9 , 19)}$

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 $\text{(3 , 7)}$ and $\text{(9 , 19)}$ into slope intercept form

  $x_1=3$

  $y_1=7$

  $x_2=9$

  $y_2=19$

Using slope formula to calculate slope of pair of points

  $m=\frac{19-7}{9-3}$

So,

  $m=\frac{12}{6}$

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 $\text{(3 , 7)}$ taken to calculate Y-intercept

  $7=2(3)+b$

So,

  $7-6=b$

On solving,

  $b=1$

Substituting value of b and m in the slope intercept form

  $y=(2)x+1$

So,

  $y=2x+1$

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