MATH SOLVE

3 months ago

Q:
# Write the point slope form of the line that passes through (-8,2) and is parallel to a line with a slope of -8. include all your work in your answer.

Accepted Solution

A:

Answer:
The point slope form of the line that passes through (-8,2) and is parallel to a line with a slope of -8 is 8x + y + 62 = 0
Solution:
The point slope form of the line that passes through the points [tex]\left(x_{1} y_{1}\right)[/tex] and parallel to the line with slope βmβ is given as Β [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex] --- eqn 1
Where βmβ is the slope of the line. Β
[tex]x_{1} \text { and } y_{1}[/tex] are the points that passes through the line.
From question, given that slope βmβ = -8
Given that the line passes through the points (-8,2).Hence we get
[tex]x_{1}=-8 ; y_{1}=2[/tex]By substituting the values in eqn 1, we get the point slope form of the line which is parallel to the line having slope -8 can be found out.
y-2=-8(x-(-8))
On simplifying we get
y β 2 = -8(x +8)
y β 2 = -8x -64
y β 2 +8x +64 = 0
8x + y +62 = 0
Hence the point slope form of given line is 8x + y +62 = 0