Answer:
The equation of the line that is parallel to given line and passes through the point (-8, -3) is: [tex]y = 5x+37[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]y=5x-3[/tex]
The general form of equation of line in slope-intercept form is written as:
[tex]y = mx+b[/tex]
Here m(co-efficient of x) is the slope of the line and b is the y-intercept.
Comparing the given equation with the general form we get
m = 5
Two parallel lines have same slope so the slope of any line parallel to given line will also be 5.
Let m1 be the slope of required line parallel to y=5x-3
Then m1=5
Putting in general form
[tex]y = m_1x+b[/tex]
[tex]y=5x+b[/tex]
To find the value of b(y-intercept) the given point has to be put in the equation from which the line passes.
The point is (-8,-3)
[tex]-3 = 5(-8)+b\\-3 = -40+b\\b = -3+40\\b = 37[/tex]
Putting the value of b and m1, we get
[tex]y = 5x+37[/tex]
Hence,
The equation of the line that is parallel to given line and passes through the point (-8, -3) is: [tex]y = 5x+37[/tex]
