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kaheart [24]
2 years ago
10

In each part that​ follows, you are given an equation of a line and a point. Find the equation of the line through the given poi

nt that is perpendicular to the given line.​ (The slope of the perpendicular line is the negative reciprocal of the slope of the given line if the given line is neither vertical nor​ horizontal.)
a) y=9x, P (0, 0)
b) y=3x+4, Q (1, 2)
Mathematics
1 answer:
Semmy [17]2 years ago
4 0

Answer:

a) y=-\frac{1}{9}x

b)y-2=-\frac{1}{3} (x-1)

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and can find the slope.

Point slope:y-y_1=m(x-x_1)

a) m\neq 9 in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is m=-\frac{1}{9}.

We will substitute m=-\frac{1}{9} and x_1=0\\y_1=0.

y-0=-\frac{1}{9} (x-0)

This simplifies to:

y=-\frac{1}{9}x

b) The equation y=3x+4 follows y=mx+b. For the perpendicular line, m\neq 3. We will need to change it into its negative reciprocal which is m=-\frac{1}{3}.

We will substitute m=-\frac{1}{3} and x_1=1\\y_1=2.

y-2=-\frac{1}{3} (x-1)


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