Respuesta :

In this problem, want to find the equation of a line that will be parallel to a given function through a point.

Recall that parallel lines have the same slope.

We are given the line

[tex]y=-1[/tex]

and the point

[tex](-5,4)[/tex]

Notice that the equations is technically in slope-intercept form, by the value of the slope will be 0:

[tex]y=0x-1[/tex]

Therefore, the slope of the line through (-5,4) will also be zero. We can use that information to find the equation.

Using the form

[tex]y=mx+b[/tex]

we can substitute the point and the slope to solve for b:

[tex]\begin{gathered} 4=0(-5)+b \\ \\ 4=b \end{gathered}[/tex]

So, the equation of our line is:

[tex]y=0x+4\text{ or }\boxed{y=4}[/tex]