Find the equation in terms of x for a line that passes through the two points (-1,3) and (4,-5)

Slope = (y2 - y1)/(x2 - x1)

Slope = (-5 - 3)/(4 + 1)

Slope = -8/5

Since the slope is equal to -8/5, use -8/5 and one of the points in the equation

(y - y1) = m(x - x1)

where m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point.

(y - 3) = -8/5(x + 1)

y - 3 = -8/5x - 8/5

y = -8/5x - 8/5 + 15/5

y = -8/5x + 7/5

That's the answer. If you check with the other point, it will go like this:

(y + 5) = -8/5(x - 4)

y + 5 = -8/5x + 32/5

y = -8/5x + 32/5 - 25/5

y = -8/5x + 7/5

Same answer.



ANSWER

y = -8/5x + 7/5

y=mx+b <- terms of x? never was good at definitions in math but was able to get to multivariable calculus, so here we go.

m=rise over run

Rise =(y2-y1) (-5-3)=-8
run=(x2-x1) (4-(-1))=5

m=(-8)/5 or -1.6 or -1(3/5)

so now we have y=1.6x+b

we have coordinates for x and y and thier relationship (m) all we have to do is plug one of the coordinates into our equation and solve for b
y2 x2
-5=(-1.6*4)+b

-5=-6.4+b
-5-(-6.4)=b
b=1.4
y=-1.6x+1.4

m = (3+5) / (-1-4) = -8/5
Point slope form gives y-3 = (-8/5)(x+1)
y = (-8/5)x +(3 - 8/5) = (-8/5)x + 7/5 or y=(7-8x)/5

y2-y1 = x2(m-x1)^2