Question

write the equation in slope intercept form for a line that will pass through (0,3) and have a slope of (-8,15)

Answer 1

The equation of line with the slope m in the slope intercept form is :

y = mx + b

Slope can express as :

`\text{ Slope=}(y_2-y_1)/(x_2-x_1)`

Substitute the value :

`(x_1,y_1)=(0,3),(x_2,y_2)=(-8,15)`

`\begin{gathered} \text{ Slope=}(y_2-y_1)/(x_2-x_1) \\ Sl\text{ope=}(15-3)/(-8-0) \\ \text{ slope=}(12)/(-8) \\ \text{slope}=(3)/(-2) \end{gathered}`

Substitute the value of slope in the equation of line:

`\begin{gathered} y-3=(3)/(-2)(x-0) \\ y-3\text{ =-}(3)/(2)x \\ y=-(3)/(2)x+3 \end{gathered}`

Equation of line in slope intercept form is :

y = -3/2x + 3

Slope = -3/2

Answer : y = -3/2x + 3

Slope = -3/2