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

Step-by-step explanation:

1. Approach,

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

Where () is the slope of the line, also known as the change in the line and 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.

Substitute in the slope,

Substitute in the point,

Simplify,

Inverse operations,

3. Putting it all together,

Now, that one has y-intercept, (); use the given slope and the formula ,  substitute in all the information.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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