Write the slope-intercept form of the equation of the line through the given point with the given slope. through (4, -2), slope = 3/4

Answer 1

Hello Delanie!

For this question, it gives us all the necessary components needed to assemble our line through slope intercept form.

Recall that slope intercept form is: y = mx + b, where the only things we need to fill in is 'm' and 'b'

and we have the following from our given premise: slope = m = 3/4 and a point (4,-2)

Since 'm' is given to us (m = 3/4), we now turn our attention to solving for 'b'.

From what we are given, we can simply plug in everything and isolate 'b'.

y = mx + b

(-2) = (3/4)*(4) + b by plugging in our slope 'm' = 3/4 and our point (x,y) = (4,-2)

-2 = (12/4) + b by the product of (3/4)*4 = 12/4

-2 = 3 + b by reducing 12/4 into simpler terms

-2 - 3 = b by moving 3 to the left hand side (through subtraction of -3 to both sides) to isolate 'b'

-5 = b since -2 - 3 = -5

Now, we have all of our components needed to assemble our line in slope intercept form.

b = -5, m = 3/4

Plugging those into y = mx + b

We now have: y = (3/4)x - 5

Hope this helps!

Answer 2

Start with point slope form

(y + 2) / (x - 4) = 3/4

Transform into slope intercept form (from Algebra 1) and answer