Find the equation of the line that is perpendicular to the line 5x + y = 4 and has the same y-intercept as 3x + 2y = 16

Answer 1

5x+y = 4 is the same as y=-5x+4 in slope intercept form, which has slope =-5. A perpendicular line has the negative inverse of -5 = 1/5 = slope

3x+2y=16 is the same as y=(16-3x)/2 = -(3/2)x + 8 which has y intercept = 8

a line with perpendicular slope and same y intercept is

y= x/5 + 8 or multiply by 5 to eliminate the fraction

5y= x + 40 or

5y-x = 40

Answer 2

Convert 5x + y = 4 to slope-intercept form

Slope of perpendicular is negative reciprocal of slope from above.

Convert 3x + 2y = 16 to slope-intercept form.

Use slope from first equation and intercept from second into point-slope form.