Question

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.

(-4, 2); y = -x+6

Answer 1

Slope-intercept form of equation of the line:

y = mx + b

y = -x + 6 ⇒ slope m₁ = -1

perpendicular line's slope:
`m_2=(-1)/(m_1) = (-1)/(-1)=1`

If line of equation y = mx + b passes through a ponit (x₀, y₀) then equation: y₀ = mx₀ + b is true.

So:

2 = 1×(-4) + b

2 = -4 + b

b = 6

Therefore:

The equation in slope-intercept form for the line that passes through the point (-4, 2) and is perpendicular to the graph of the equation y=-x+6 is:

y = x + 6