Question

Find the equation of the line through the points (4,-13) and (-9,39) in slope intercept form

Answer 1

To find the equation of the line, we will first find the slope

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

(4,-13) and (-9,39)

x₁=4 y₁=-13 x₂=-9 y₂=39

substitute into the formula

`\text{slope}=(39+13)/(-9-4)`

`=(52)/(-13)`
`=-4`

Find the intercept (b) by substituting slope(m)=-4 and x₁=4 y₁=-13 into y=mx + b and then solve for b

-13 = -4(4) + b

-13 = -16 + b

Add 16 to both-side

-13 + 16 = b

3 = b

b= 3

Form the equation by substituting m =-4 and b = 3 in y=mx + b

y= -4x + 3