Question

Write the equation of the line that passes through the give points (-1,11) and (3,-5)

Answer 1

`y=-4x+7`

Explanation:

Use the slope-intercept formula:
`y=mx+b` where m is the slope and b the y-intercept.

Find the slope using the slope formula for when you know two points:

`(-1,11)(3,-5)\\\\(-1(x1),11(y1))\\(3(x2),-5(y2))\\\\(y(2)-y(1))/(x(2)-x(1))`

Insert values:

`(-5-11)/(3-(-1))`

Simplify parentheses:

`(-5-11)/(3+1)`

Simplify:

`(-16)/(4) =-4`

Insert into equation:

`y=-4x+b`

Find the y-intercept by taking one of the points and inserting into the equation:

`(3,-5)\\(3(x),-5(y))\\-5=-4(3)+b`

Solve for b

`-5=-4*3+b\\-5=-12+b\\-5+12=-12+12+b\\-5+12=b\\7=b`

7 is the y-intercept. Insert into the equation:

`y=-4x+7`

Done.

Answer 2

Explanation:

Points: (-11,11) (3,-5)

Slope equation: y=mx+b

m (slope): (11- -5)/(-11-3) = 16/-14 = -8/7

y=(-8/7)x+b

Plug in one of the points.

-5=(-8/7)(3)+b

-5=-3.4+b

b=1.6

Final Equation:

y=(-8/7)+1.6

(These answers are rounded to the nearest tenth)