Question

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

Answer 1

Step-by-step explanation:

$m = - \frac{2}{3} \\ ( - 10 ,\: 8) = (x_1,y_1)$

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

Plug in the values into the equation

$y - 8 = - \frac{2}{3} (x - ( - 10)) \\ y - 8 = - \frac{2}{3}( x + 10)$

$y - 8 = - \frac{2}{3} x - \frac{20}{ 3 } \\ y = - \frac{2}{3} x - \frac{20}{3} + 8$

$y = - \frac{2}{3} x + \frac{4}{3}$

To solve for x-intercept , Arrange the values in

$ax + by + c = 0$

=

$- \frac{2}{3} x - y + \frac{4}{3} = 0$

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

$- \frac{2}{3} x - y + \frac{4}{3} = 0 \\ - \frac{2}{3} x - 0 + \frac{4}{3} = 0$

$- \frac{2}{3} x + \frac{4}{3} = 0 \\ - \frac{2}{3} x = - \frac{4}{3}$

Solve for x ;

$x = 2$

To find y intercept , let x = 0

and solve for y .

I hope it helps <3

Answer 2

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)