Question

what is the equation in slope intercept form of the line that passes through the point (-4,47) and (2,-16)

Answer 1

y= -21/2x+5

Explanation:

Answer 2

The slope-intercept form:

`y=mx+b`

The formula of a slope:

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

We have the points (-4, 47) and (2, -16). Substitute:

`m=(-16-47)/(2-(-4))=(-63)/(6)=-(63:3)/(6:3)=-(21)/(2)`

Therefore we have:

`y=-(21)/(2)x+b`

Put the coordinates of the point (2, -16) to the equation:

`-16=-(21)/(2)(2)+b\\\\-16=-21+b\qquad\text{add 21 from both sides}\\\\5=b\to b=5`

Answer:
`\boxed{y=-(21)/(2)x+5}`