Key Concepts
- Perpendicular lines
- Linear equations
- Slope-intercept form
Linear equations are often organized in slope-intercept form: [tex]y=mx+b[/tex]
To find a linear equation, we often first solve for the slope, and then solve for the y-intercept algebraically.
To find the slope of a perpendicular line, we must find the negative reciprocal of the slope of the reference line.
Solving the Question
We're given:
- Reference line is [tex]y=-x[/tex]
- Perpendicular line passes through [tex](-8,2)[/tex]
1) Find the slope of the reference line
We can rewrite the reference line to be clearer in slope-intercept form:
[tex]y=-1x+0[/tex]
This means that -1 is the slope.
2) Find the slope of the perpendicular line
The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular line is 1. Plug this into slope-intercept form:
[tex]y=x+b[/tex]
3) Solve for the y-intercept of the perpendicular line
[tex]y=x+b[/tex]
Plug in the given point (-8,2) and solve for b:
[tex]2=-8+b\\b=2+8\\b=10[/tex]
Therefore, the y-intercept of the perpendicular line is 10. Plug this back into our original equation:
[tex]y=x+10[/tex]
Answer
[tex]y=x+10[/tex]
