Question

Write a slope-intercept equation for a line passing through the point (4,7) that is parallel to y=x+1. Then write a

second equation for a line passing through the given point that is perpendicular to the given line.

Answer 1

y = x + 3

y = -x + 11

Explanation:

When the slopes are parallel they are the same. When slopes are negative, the slope is the negative reciprocal.

Parallel: The slope is 1. This is the coefficient of the x in the equation given. If you do not see a number before the x like in y = x + 1, then number is 1.

Use this form:

y =mx + b Us the slope of 1 to put in for m. Use 4 for x and 7 for y

7 =(1)4 + b Solve for b.

7 = 4 + b Subtract 4 from both sides.

3 = b

The equation for the parallel line is

y = x + 3.

Perpendicular:

y = mx + b This time the slope is -1 Still use 4 for x and 7 for y

7 = (-1)4 + b

7 =-4 + b add 4 to both sides

11 = b

The equation would be y = -x + 11