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 point 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)

a)

b)

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:

a) in our new equation because it is perpendicular to it. This means we will need to change it into its negative reciprocal which is .

We will substitute and .

This simplifies to:

b) The equation y=3x+4 follows y=mx+b. For the perpendicular line, . We will need to change it into its negative reciprocal which is .

We will substitute and .

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step-by-step explanation: