Question

2x + 5y= 10; (4,9)
Write answer in slope intercept form.

Answer 1

y = 5x - 5/2xy + 79

Explanation:

First we need to solve for m which is slope.

Subtract 5y from both sides

2x = 10 - 5y

Then divide each term by 2

2x/2 = 10/2 + -5y/2

Then simplify to the left

x = 10/2 + -5y/2

Then simplify the right side

x = 5 - 5y/2

Next we have to find the value of b using the formula y = mx + b

So

y = (5 - 5y/2) * x + b

y = (5 - 5y/2) * (4) + b

9 = (5 - 5(9)/2) * (4) + b

Rewrite

(5 - 5(9)/2) * 4 + b = 9

Simplify more

Multiply 5 by 9

(5 - 45/2) * 4 + b = 9

Multiply by 2/2 to write 5 as a fraction

5 * 2/2 - 45/2) * 4 + b = 9

Then combine 5 and 2/2

(5 * 2/2 - 45/2) * 4 + b = 9

Combine the numerator over the denom

5 * 2 - 45/2 * 4 + b = 9

Simplify the numerator

-35/2 * 4 + b = 9

Cancel the common factor of 2

-35 * 2 + b = 9

Multiply

-70 + b = 9

Move the terms without b to the right side

b = 9 + 70 > b = 79

Now we substitute all the values into y = mx + b

y = 5x - 5/2xy + 79