Question

Answer please cuz I'm very confused

Answer 1

5x + 3y = - 53

the equation of a line in ' slope- intercept form ' is y = mx + c

where m is the slope and c the y-intercept

rearrange 3x - 5y = - 15 into this form to obtain m → (subtract 3x from both sides)

- 5y = - 3x - 15 → divide all terms by - 5 )

y = $\frac{3}{5}$ x + 3 → in slope-intercept form with m = $\frac{3}{5}$

given a line with slope m then the slope m₁ of a line perpendicular to it is

m₁ = - $\frac{1}{m}$ = - 1 ÷ $\frac{3}{5}$ = - $\frac{5}{3}$

partial equation is y = - $\frac{5}{3}$ x + c

to find c substitute ( - 7, - 6) into the partial equation

- 6 = $\frac{35}{3}$ + c ⇒ c = - 6 - $\frac{35}{3}$ = - $\frac{53}{3}$

y = - $\frac{5}{3}$ x - $\frac{53}{3}$ → in slope intercept form

multiply all terms by 3

3y = - 5x - 53 → ( add 5x to both sides )

5x + 3y = - 53 → in standard form