Write the equation of the line that goes through the points (8, -7) and (5, -3).

Answer 1

Start by finding the slope using the slope formula which is Δy/Δx

Using the slope and one of the points, substitute values into the point-slope formula: y-y1=m(x-x1)

In the formula the y1 &x1 represent the x,y values of the point you chose. Whereas the y & x without the labels are variables in our equation of the line y=Mx+b and will remain y & x

So the slope calculates to 4/-3 or negative four thirds.

using (8,-7) as my point you plug into the point slope formula.

y-(-7)=-4/3x-8 OR y+7=-4/3x-8

isolate the y variable by subtracting 7 from both sides to get y=Mx+b format

y=-4/3-1

Answer 2

Hi.

When you have two points and need to find the equation, it’s best to first find the slope between the two points.

(8,-7)

(5,-3) m = -3 - (-7) / 5 - 8

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

m = (4 / -3)

Now put it into point slope form: y - y₁ = m ( x - x₁ )

Plug in (8,-7) into the equation : y - (-7) = (-4/3)(x - 8)

: y +7 = (-4/3)(x-8)

Now make it slope intercept form: y= mx+b

y+7= (-4/3)x -8(-4/3)

y+7 = (-4/3)x + 32/3

y+ (21/3) = (-4/3)x + 32/3

-(21/3) -(21/3)

y= (-4/3)x + (11/3)