algebra question

Question

Two lines are perpendicular if either the product of their slopes is −?1, or one line is vertical and the other horizontal. Write an equation of the line perpendicular to the line given by 3x-4y=8 and having the same? y-intercept as the line given by 4x+6y=18.

Answer 1

You may either (1) convert the given equation of a line into slope-intercept form (y=mx+b), use (-1/m) for the slope of the perpendicular line, then include the same y-intercept, or (2) you may convert the Standard Equation of a line (Ax+By=C) once and forever to slope-intercept form and remember that the slope is (-A/B), so the slope of the perpendicular line is (B/A); also the y-intercept is (C/B).

 

The line  3x-4y=8 has a slope of (3/4) and all perpendicular lines have a slope of (-4/3).

The y-intercept of the line 4x+6y=18  (or, 2x+3y=9) is 18/6 or 9/3=3.

 

The equation of the line is  4x+3y=9  in Standard Format and y=(-4/3)x +3 in slope-intercept format.

 

Note: since the problem gives the lines in Standard Format, that might be the preferred format for the answer.

Answer 2

4x + 6y = 18

6y = -4x + 18      subtract 4x from both side

y = -4x/6 + 3       divide both sides by 6

The y-intercept is 3

 

3x - 4y = 8

- 4y = -3x + 8      subtract 3x form both sides

y = 3x/4 - 2

The slope is 3/4

 

Equation of perpendicular line

y = -4x/3 + 3