Chapter SH, Problem 4.14EP

To determine

To write an equation in slope intercept form for the line that passes through point $(-1,6)$ and parallel to $y=\frac{1}{4}x-4$ .

Answer to Problem 4.14EP

The slope intercept form is $y=\frac{1}{4}x+\frac{25}{4}$ .

Explanation of Solution

Given information:

The line that passes through point $(-1,6)$ and parallel to $y=\frac{1}{4}x-4$

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.

From equation $y=\frac{1}{4}x-4$

Slope

  $=\frac{1}{4}$

As line is parallel to $y=\frac{1}{4}x-4$

Then, the slope of line is equal to slope of line ( $y=\frac{1}{4}x-4$ )

Then, slope of required line

  $=\frac{1}{4}$

Line passes through point $(-1,6)$

Slope intercept form of line when slope and a point is given

  $y-6=\frac{1}{4}(x-(-1))$

So,

  $y-6=\frac{1}{4}x+\frac{1}{4}$

On solving,

  $y=\frac{1}{4}x+\frac{25}{4}$

Hence, the slope intercept form is $y=\frac{1}{4}x+\frac{25}{4}$ .