Answer:
Part 1) The slope of the line that is parallel to the given line is [tex]m=-\frac{1}{4}[/tex]
Part 2) The equation, in point-slope form, of the line that is parallel to the given line and passes through the given point is
[tex]y+4=-\frac{1}{4}(x+2)[/tex]
Part 3) The y-intercept is the point (0,-4.5)
Step-by-step explanation:
Part 1) What is the slope of the line that is parallel to the given line and passes through the given point?
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-6,8) and (2,6)
substitute
[tex]m=\frac{6-8}{2+6}[/tex]
[tex]m=-\frac{1}{4}[/tex]
step 2
Find the slope of the line that is parallel to the given line
we know that
If two lines are parallel, then their slopes are equal
so
The slope of the line that is parallel to the given line is also
[tex]m=-\frac{1}{4}[/tex]
Part 2) What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?
we know that
The equation of the line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{4}[/tex]
[tex]point\ (-2,-4)[/tex]
substitute
[tex]y+4=-\frac{1}{4}(x+2)[/tex]
Part 3) What is the y-intercept of the line that is parallel to the given line and passes through the given point?
we know that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
substitute in the linear equation
[tex]y+4=-\frac{1}{4}(0+2)[/tex]
solve for y
[tex]y+4=-0.5\\y=-4.5[/tex]
therefore
The y-intercept is the point (0,-4.5)
