Question

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

Answer 1

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

$y-y_1=m(x-x_1)$

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

$\boxed{y-5=4(x-7)}$

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:

$y=mx+b$

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.

$y-5=4(x-7)$

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

$y-5=4x-28$

Now, add 5 to both sides of the equation

$\boxed{y=4x-23}$

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! :)