Question

(3,-8),(-2,5) write an equation for the line in point slope form .Then rewrite the equation in slope intercept form

Answer 1

The equation for the line in point-slope form is:

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

Where m is the slope and (x1, y1) is a point of the line. If we have two points (x1,y1) and (x2, y2), the slope is equal to:

`m=(y_2-y_1)/(x_2-x_1)`

So, replacing (3, -8) and (-2, 5), we get that the slope and the equation of the line are:

`m=(5-(-8))/(-2-3)=(5+8)/(-5)=(-13)/(5)`
`\begin{gathered} y-(-8)=(-13)/(5)(x-3) \\ y+8=-(13)/(5)(x-3) \end{gathered}`

Therefore, the equation in slope-intercept form is calculated as:

`\begin{gathered} y+8=-(13)/(5)x-(13)/(5)\cdot(-3) \\ y+8=-(13)/(5)x+(39)/(5) \\ y=-(13)/(5)x+(39)/(5)-8 \\ y=-(13)/(5)x-(1)/(5) \end{gathered}`

Answer: Point-slope form:

`y+8=-(13)/(5)(x-3)`

slope-intercept form:

`y=-(13)/(5)x-(1)/(5)`