Write the point-slope form, then use that to write the slope-intercept form of the equation

For a line with slope m that passes through a point [tex](x_1, y_1)[/tex], the point-slope form equation is the following.

[tex]y-y_1=m(x-x_1)[/tex]

We have a given slope of 4 and a given point of (7,5). Now, plug in the values.

[tex]\boxed{y-5=4(x-7)}[/tex]

That is the point-slope form of the line. Now, let's change this into slope-intercept form. Slope-intercept form looks like the following:

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

Where m is the slope and b is the y-intercept. Let's do some algebra on our point-slop form equation to change it into slope-intercept form.

[tex]y-5=4(x-7)[/tex]

This was our equation. Let's use the distributive property on 4(x-7).

[tex]y-5=4x-28[/tex]

Now, add 5 to both sides of the equation

[tex]\boxed{y=4x-23}[/tex]

This the slope-intercept form of the line. Thus, we have solved for both the point-slope form and the slope-intercept form. Hope this helps! :)