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! :)
