Question

What is the equation of the line that passes through the point (8, -4) and has a slope of 1/2

Answer 1

Answer:

$y = \frac{1}{2}x - 8$

Step-by-step explanation:

1. Approach,

For this problem, the format of a line that will be used is, slope-intercept form;

$y = mx + b$

Where ($m$) is the slope of the line, also known as the change in the line and $(b)$ is the y-intercept, or where the graph of the line intersects the y-axis. Since, in this problem, the slope of the line is given, all one has to do is substitute in a point on the given line and solve.

2. Finding the equation,

In this problem, the slope of the line is given. Therefore, to solve this problem, all one has to do is substitute in a point on the given line and solve.

$y = mx + b$

Substitute in the slope,

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

Substitute in the point,

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

Simplify,

$-4 = 4 + b$

Inverse operations,

$-4 = 4 + b\\-4\\\\-8 = b$

3. Putting it all together,

Now, that one has y-intercept, ($-8$); use the given slope and the formula $y = mx + b$,  substitute in all the information.

$y = \frac{1}{2}x - 8$