Question

What is the slope-intercept form of the equation of the line perpendicular to y = -x + 10 and passing throught the point (-2,7)?

Oy+7= -(– 2)
Oy-7= -12 +2)
O y = -x + 6
O y= 22 +5

Answer 1

The slope-intercept form equation of the line perpendicular to y =
`-(1)/(2)` x + 10 and passes through point (-2, 7) is y = 2x + 11 ⇒ Not in the choices

Explanation:

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept

The product of the slopes of the perpendicular lines is -1, if the slope of one is m, then the slope of the other is
`-(1)/(m)`

• To find the slope of the perpendicular line to a given line reciprocal the slope of the given line and change its sign

∵ The equation of the given line is y =
`-(1)/(2)` x + 10

→ Compare it with the form of the equation above

∴ m =
`-(1)/(2)`

→ Reciprocal it and change its sign to get the slope of the ⊥ line

∴ m⊥ = 2

→ Substitute in the form of the equation above

∴ y = 2x + b

→ To find b substitute x and y in the equation by the coordinates of

a point on the line

∵ The line passes through the point (-2, 7)

∴ x = -2 and y = 7

∵ 7 = 2(-2) + b

∴ 7 = -4 + b

→ Add 4 to both sides to find b

∵ 7 + 4 = -4 + 4 + b

∴ 11 = b

→ Substitute it in the equation

∴ y = 2x + 11

The slope-intercept form equation of the line perpendicular to y =
`-(1)/(2)` x + 10 and passes through point (-2, 7) is y = 2x + 11

Note: The answer is not in the choices