Question

Find the equation of the line with slope =-7 and passing through (-4,-5) .write your equation in point slope and slope intercept forms

Answer 1

Point-slope form:

y - y₁ = m(x - x₁)         "m" is the slope

You know:

m = -7

(-4 , -5) = (x₁ , y₁)

Plug these into the equation:

y - y₁ = m(x - x₁)

y - (-5) = -7(x - (-4))

y + 5 = -7(x + 4)

Slope-intercept form:

y = mx + b       "m" is the slope, "b" is the y-intercept (the y value when x = 0)

You can solve this two ways:

#1:  Since you know m = -7, plug it into the equation

y = mx + b

y = -7x + b

To find "b", plug in the point (-4, -5) into the equation

y = -7x + b

-5 = -7(-4) + b

-5 = 28 + b    Subtract 28 on both sides

-33 = b

y = -7x - 33

#2: Use the point-slope form and change it to slope-intercept form by isolating/getting "y" by itself.

y + 5 = -7(x + 4)     First distribute/multiply -7 into (x + 4)

y + 5 = -7x - 28     Subtract 5 on both sides

y = -7x - 33