Chapter 3.4, Problem 36PPS

To determine

To write an equation of line whose x- intercept is $-\frac{1}{2}$ and y -intercept is $4$ in slope intercept form.

Answer to Problem 36PPS

Slope intercept form

  $y=8x+4$

Explanation of Solution

Given information:

x- intercept of line is $-\frac{1}{2}$

And y -intercept of line is $4$

Formula used:

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

Point-slope form

  $y-y_1=m(x-x_1)$

Slope intercept form

  $y=mx+b$

Calculation:

x- intercept of line $=-\frac{1}{2}$

y -intercept of line is $=4$

Here

x- intercept means y-coordinate will be zero

y -intercept means x -coordinate will be zero

Then rewrite x and y intercept in coordinate form

x- intercept of line $=\left(-\frac{1}{2},0\right)$

y -intercept of line is $=(0,4)$

Here

  $x_1=-\frac{1}{2}$

  $y_1=0$

  $x_2=0$

  $y_2=4$

Using slope formula to calculate slope of line

  $m=\frac{4-0}{0-\left(-\frac{1}{2}\right)}$

On solving

  $m=\frac{4}{\frac{1}{2}}$

On solving

  $m=8$

Using slope and any one of the point to find slope intercept form

  $m=8$

Let take point $(0,4)$

Here

  $x_1=0$

  $y_1=4$

Point-slope form

  $y-4=8(x-0)$

On solving

  $y-4=8x$

Add 4 both sides

  $y-4+4=8x+4$

On solving

  $y=8x+4$

Hence, slope intercept form is $y=8x+4$