slope and intercept equation

Question

Write an equation of the line that passes through the given point
and has the given slope. Write your equation in slope-intercept form.

(10,-8);m=3/5

Answer 1

Given point (10,-8) and slope m=3/5

LIne passes through the point (x₁ , y₁) =( 10, -8)

Formula of the line equation is (y - y_{1) =}m (x - x₁ )

Substitute the point (10,-8) and slope m=3/5 in formula

(y - (-8) ) ₌ 3/5 (x - 10 )                     (-(-8) = 8 )

(y + 8) ₌ 3/5 (x - 10 )                        ( Multiply each side by 5 )

5(y + 8) ₌ 3/5×5 (x - 10 )                   ( 3/5×5 =3)

5(y + 8) ₌ 3 (x - 10 )                         (simplify)

5y + 40  = 3x -30                             (Subtract each side by 40 )

5y + 40 -40  = 3x -30 -40                  (simplify)

5y = 3x -70                                      (Divide  each side by 5 )

5y/5 = 3x/5 -70/5                              (simplify)

y = 3x/5 - 14

The slope intercept equation is y = 3x/5 - 14.

Comments

• Point - slope - form of a line equation is y - y_{1 =} m(x - x₁), where m is slope, and (x_1, y₁) is the point lies on the line.
• Slope - intercept - form of a line equation is y = mx + b, where m is slope, and b is y - intercept.