Question

Enter the slope-intercept equation of the line that has the same slope as y - 3 = (x + 3) and contains

Answer 1

Given:

$y-3=\frac{1}{2}(x+3)$

Point = (8, 4)

To find:

The slope-intercept form of the equation of the line.

Solution:

$y-3=\frac{1}{2}(x+3)$

Slope of this line = $\frac{1}{2}$.

Slope of the line is same as the slope of  $y-3=\frac{1}{2}(x+3)$.

Slope of the line (m) = $\frac{1}{2}$

General form of line:

y = mx + b

$y=\frac{1}{2} x+b$ ---------- (1)

It contains the point (8, 4). Substitute x = 8 and y = 4 in (1).

$4=\frac{1}{2}( 8)+b$

$4=4+b$

Subtract 4 from both sides, we get

b = 0

Substitute b = 0 in (1).

Equation of the line:

$y=\frac{1}{2} x+0$

$y=\frac{1}{2} x$

Complete the sentence:

$y=\frac{1}{2} x$; I used the general form of a line in slope-intercept form, y = mx + b. The slope, m is $\frac{1}{2}$. Then I substituted 8 for x and 4 for y into the standard form and solved for b, which is 0.