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3 years ago

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

Mathematics

1 answer:

notka56 [123]3 years ago

6 0

Answer:

The slope-intercept form equation of the line perpendicular to y = $-\frac{1}{2}$ 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

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 $-\frac{1}{m}$

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 = $-\frac{1}{2}$ x + 10

→ Compare it with the form of the equation above

∴ m = $-\frac{1}{2}$

→ 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 = $-\frac{1}{2}$ x + 10 and passes through point (-2, 7) is y = 2x + 11

<u><em>Note:</em></u> The answer is not in the choices

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