Question

write the slope-intercept form of the equation of a line passing through the following two points: (-3, 7) & (6, -5)

Answer 1

Answer:
`y = -(4)/(3) x +3`

In order to find equation, first find slope:

`\sf slope : (y_2 - y_1)/(x_2 - x_1) \quad where \ (x_1, y_1) , \ (x_2, y_2) \ are \ points`

Given points: (-3, 7) and (6, -5)

`\rightarrow \sf slope : (-5-7)/(6-(-3)) =-(4)/(3)`

Equation:

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

insert values

`\rightarrow \sf y - 7 = -(4)/(3) (x -(-3))`

`\rightarrow \sf y = -(4)/(3) x - 4 +7`

`\rightarrow \sf y = -(4)/(3) x +3`