I need help with this algebra 1 question

Question

What is the equation in standard form of the line that passes through the point (3,-9) and has a slope of 1/3

Answer 1

If use slope-intercept form: y = mx + b (m = slope = rise/run); b is y-intercept.

Point is (3, -9); slope = 1/3

-9 = 3/3 + b → -9 = 1 + b → b = -10

so y = 3/x - 10. Need chg to std form. Mult by 3

3y = x - 30 → x - 3y = 30

Using point-slope form: y₂ - y₁ = m(x₂ - x₁)

y - (-9) = 1/3(x - 3) →y + 9 = x/3 -1

Mult by 3 to elim fraction; 3y +27 = x - 3 → x - 3y = 30

Check on Desmos Graphing Calculator website.

Answer 2

Use the definition of slope

(y + 9) /. (x - 3) = 1 / 3