# 9.5.4. Equation of the Straight Line Given Its Slope and Its y–Intercept

Find, in the form of , the equation of the straight line that intercepts 20 length units from the negative part of the -axis and is perpendicular to the straight line whose equation is .

• A
• B
• C
• D

### Example

Find, in the form of , the equation of the straight line that intercepts 20 length units from the negative part of the -axis and is perpendicular to the straight line whose equation is .

### Solution

We know that equations for straight line graphs can be written in the form , where is the slope and is the -intercept.

First, rearrange into the form .

Comparing this equation to , we can see that the slope of the line is .

Then find the slope, , of the required line.

We know also that if 2 straight lines, and , having slopes and are perpendicular, then .

So, we know that .

Therefore,

The slope of the required line is , so its equation is where is the -intercept.

Then find the -intercept.

We are told in the question that the line crosses the -axis at the point with coordinates . This point must satisfy the equation of the line, so we have

Therefore,

Substituting for in the equation gives us the equation of the required line.

0
correct
0
incorrect
0
skipped