Question

A line has a slope of -2/3 and passes through the point -3,8 how do I get the equation ?

Answer 1

The equation of the line in slope-intercept form is;

`y=-(2)/(3)x+6`

Step-by-step explanation:

We want to find the equation of the line with the slope and a point given.

`\begin{gathered} \text{slope m=}(-2)/(3) \\ \text{ point (-3,8)} \end{gathered}`

Recall that the point-slope equation of a straight line is of the form;

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

substituting the given slope and point into the equation and simplifying;

`\begin{gathered} y-8=-(2)/(3)(x-(-3)) \\ y-8=-(2)/(3)(x+3) \\ y=-(2)/(3)x-(2)/(3)(3)+8 \\ y=-(2)/(3)x-2+8 \\ y=-(2)/(3)x+6 \end{gathered}`

Therefore, the equation of the line in slope-intercept form is;

`y=-(2)/(3)x+6`