Question

Say you are given the graph of the line y = -x. Write the equation of the line that is perpendicular to the given line and goes through the point (-8, 2).

Answer 1

Key Concepts

• Perpendicular lines
• Linear equations
• Slope-intercept form

Linear equations are often organized in slope-intercept form:
`y=mx+b`

• m = slope
• b = y-intercept

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
  `y=-x`
• Perpendicular line passes through
  `(-8,2)`

1) Find the slope of the reference line

We can rewrite the reference line to be clearer in slope-intercept form:

`y=-1x+0`

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:

`y=x+b`

3) Solve for the y-intercept of the perpendicular line

`y=x+b`

Plug in the given point (-8,2) and solve for b:

`2=-8+b\\b=2+8\\b=10`

Therefore, the y-intercept of the perpendicular line is 10. Plug this back into our original equation:

`y=x+10`

Answer

`y=x+10`