Find the equation of the line with slope = -8 and passing through (7,-53)

Answer 1

Solution:

The equation of the line can be found by knowing the slope and one point passing through the line.

The slope form of the equation m = Δy / Δx = y -y1 / x - x1, -8 = y -(-53) / x - 7 = y +53 / x-7 cross multiply and

solve for y, y + 53 = -8(x - 7) , y + 53= -8x + 56 , y = -8x + 56 -53 = -8x + 3 , and the equation is

y = -8x + 3 and if you examine this equation it is of the form y = m x+ b , where m is the slope = -8 and b=3 is the y intercept

Answer 2

The equation of a line is y= mx + b (slope-intercept form)

Since you already know the slope, we will plug it in for m --> y = -8x + b

We need the y-intercept, which is where the line crosses the y-axis. Plug in the ordered pair that we know is on the line (7, -53) for the x and y in the equation. That leaves the only variable as b, so we can then solve for b.

y = -8x + b

-53 = -8(7) + b

-53 = -56 + b

3 = b

Rewrite the equation using only the slope and y-intercept --> y = -8x + 3