Question

Write a point-slope equation for the line that passes through the point (11,16)

and is parallel to the line given by y = 9x + 41.Do not use parenthesis on the y-
side.

Answer 1

Explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

y = 9x + 41

Comparing with the slope intercept form, slope = 9

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (11, 16) is 9

To determine the intercept, we would substitute m = 9, x = 11 and y = 16 into y = mx + c. It becomes

16 = 9 × 11 + c = 99 + c

c = 16 - 99

c = - 83

The equation becomes

y = 9x - 83

Answer 2

Explanation:

y=kx+n

k=9 because it is parallel to the line y=9x+41.

For x=11, y must be 16, so we have

16=9*11+n

16=99+n

n=-83.

So we have y=9x-83.