Question

A line with a slope of -2/5 that passes through the point (-10,8)

Answer 1

y = mx + b

m = -²/₃ and line pases through (-10, 8) so:

8 = -²/₃(-10) + b

8 = ²⁰/₃ + b

b = 8 - ²⁰/₃

b = 8 - 6²/₃

b = 1¹/₃

b = ⁴/₃

Slope Intercept Form:

y = -²/₃x + ⁴/₃

x-intercept:

-²/₃x + ⁴/₃ = 0

-²/₃x =- ⁴/₃

x = - ⁴/₃ ÷(-²/₃)

x = 2

(2, 0)

y-intercept:

y = -²/₃•0+ ⁴/₃ = ⁴/₃

(0, ⁴/₃)

Answer 2

Explanation:

`m = - (2)/(3) \\ ( - 10 ,\: 8) = (x_1,y_1)`

`y-y_1=m(x-x_1)`

Plug in the values into the equation

`y - 8 = - (2)/(3) (x - ( - 10)) \\ y - 8 = - (2)/(3)( x + 10) \\`

`y - 8 = - (2)/(3) x - (20)/( 3 ) \\ y = - (2)/(3) x - (20)/(3) + 8 \\`

`y = - (2)/(3) x + (4)/(3)`

To solve for x-intercept , Arrange the values in

`ax + by + c = 0`

=

`- (2)/(3) x - y + (4)/(3) = 0`

To find x-intercept .let y = 0 in the above equation

`- (2)/(3) x - y + (4)/(3) = 0 \\ - (2)/(3) x - 0 + (4)/(3) = 0 \\`

`- (2)/(3) x + (4)/(3) = 0 \\ - (2)/(3) x = - (4)/(3)`

Solve for x ;

`x = 2`

To find y intercept , let x = 0

and solve for y .

I hope it helps <3