Explanation
We have the following information:
[tex](-2,5);y=-4x+2,[/tex]
and our task is to find the slope-intercept equation of the line that passes through the given point and is parallel to the graph of the given line.
Recall that the slope-intercept equation of any line has the following "framework":
[tex]y^{\prime}=m\cdot x^{\prime}+b,_{}[/tex]
where "m" and "b" are constants called the slope of the line and the y-intercept, respectively. We want our line to be parallel to the graph of the given one; this means that the slope of both lines must be the same. Then,
[tex]m=-4.[/tex]
Then, our equation becomes
[tex]y^{\prime}=-4x^{\prime}+b\text{.}[/tex]
Now, we want the point (-2,5) to lie on the line. In other words, this point must "satisfy" our equation in the following sense:
[tex]5=-4(-2)+b\text{.}[/tex]
Solving this equation for b, we get
[tex]\begin{gathered} 5=-4(-2)+b, \\ 5=8+b, \\ 8+b=5, \\ -8+(8+b)=-8+5, \\ -8+8+b=-3, \\ b=-3. \end{gathered}[/tex]
Then, our desired equation is
[tex]y^{\prime}=-4x^{\prime}-3.[/tex]
Graphically, all looks like
(The green line represents the given one, and the blue line represents the requested line. And clearly, the orange point is the given point)
Answer
The slope-intercept equation of the line that passes through the given point and is parallel to the graph of the given line is
[tex]y^{\prime}=-4x^{\prime}-3.[/tex]
