Answer:
The slope-intercept form equation of the line perpendicular to y = [tex]-\frac{1}{2}[/tex] x + 10 and passes through point (-2, 7) is y = 2x + 11 ⇒ Not in the choices
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
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 [tex]-\frac{1}{m}[/tex]
- 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 = [tex]-\frac{1}{2}[/tex] x + 10
→ Compare it with the form of the equation above
∴ m = [tex]-\frac{1}{2}[/tex]
→ 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 = [tex]-\frac{1}{2}[/tex] x + 10 and passes through point (-2, 7) is y = 2x + 11
Note: The answer is not in the choices
