A line contains the points (8, 9) and (–12, –7). Using point-slope form, write the equation of the line that is parallel to the given line and that passes through (–5, –15).

slope of the line going through the first two points

= (-7-9)/(-12-8) = -16/-20 = 4/5

so going through new point (-5,-15) with the same slope

y+15 = (4/5)(x+5)

do whatever you have to do further, but that is in
point-slope form

udk

line passes through ( 1, -5 ) and ( -3, 7).

a.) Write an equation for the line point-slope form.

B, Rewrite the equation in slope-intercept form.

To find the equation of a line parallel to the given line and passing through a given point, we can use the point-slope form of a linear equation.

Point-slope form: y - y₁ = m(x - x₁)

First, let's find the slope (m) of the given line. The slope of a line can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the given points (8, 9) and (-12, -7):
m = (-7 - 9) / (-12 - 8)
m = -16 / -20
m = 4/5

Now, we can substitute the slope (m = 4/5) and the given point (-5, -15) into the point-slope form:

y - (-15) = 4/5(x - (-5))
y + 15 = 4/5(x + 5)

Simplifying the equation by multiplying both sides by 5 to eliminate the fraction:

5(y + 15) = 4(x + 5)
5y + 75 = 4x + 20

Rearranging the equation to the standard form (Ax + By = C):

4x - 5y = 55

Therefore, the equation of the line that is parallel to the given line and passes through (-5, -15) is 4x - 5y = 55.