Question

For questions 19-22, write a linear equation with the given information.

19. Passing through (2, 3) and PARALLEL to y = x - 4
19.
20.
20. Passing through (-6, -1) and PARALLEL 2x + 3y = 3
21.
22
21. Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5
22. Passing through (-2, -11) and PERPENDICULAR to x + 4y = 8
Gina Wilson (Al Things Algebra, LLC), 2012-2017

Answer 1

• 19. y = x + 1
• 20. y = -2/3x - 5
• 21. y = -1/2x + 7
• 22. y = 4x - 3

Explanation:

19. Passing through (2, 3) and PARALLEL to y = x - 4

Parallel lines have equal slopes:

• y = x + b

Use given point to find b:

• 3 = 2 + b
• b = 1

The line is:

• y = x + 1

20. Passing through (-6, -1) and PARALLEL 2x + 3y = 3

Rewrite in the slope-intercept form:

• 2x + 3y = 3
• 3y = -2x + 3
• y = -2/3x + 1

The line have same slope:

• y = -2/3x + b
• -1 = -2/3(-6) + b
• -1 = 4 + b
• b = - 5

The line is:

• y = -2/3x - 5

21. Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5

Perpendicular lines have negative-reciprocal slopes

The line has the form:

• y = -1/2x + b

Find the y-intercept:

• 8 = -1/2*(-2) + b
• 8 = 1 + b
• b = 7

The line is:

• y = -1/2x + 7

22. Passing through (-2, -11) and PERPENDICULAR to x + 4y = 8

Perpendicular lines have negative-reciprocal slopes

Rewrite in slope-intercept form:

• x + 4y = 8
• 4y = -x + 8
• y = -1/4x + 2

The line has the form:

• y = 4x + b

Find y-intercept:

• -11 = 4(-2) + b
• -11 = -8 + b
• b = -3

The line is:

• y = 4x - 3