Answer:
The equation of the line, using the point-slope form, through (-4,6) that is parallel to the line will be:
[tex]y=-5x-14[/tex]
Step-by-step explanation:
We know that the slope-intercept form is
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept
Given the equation
[tex]y=-5x+2[/tex]
comparing with the slope-intercept form
slope = m = -5
y-intercept = b = 2
We know that the parallel lines have the same slopes.
so
, the slope of the parallel line will be: -5
Thus, the equation of the line, using the point-slope form, through (-4,6) that is parallel to the line will be:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-6 = -5(x-(-4)[/tex]
[tex]y-6 = -5 (x+4)[/tex]
[tex]y-6 = -5x-20[/tex]
[tex]y=-5x+6-20[/tex]
[tex]y=-5x-14[/tex]
