Question

How do i solve this? - Linear Functions

Answer 1

solve for y

Explanation:

`5x-2y=-10`

subtract 5x from both sides

`5x-5x-2y=-10-5x`

`-2y=-10-5x`

Divide each term in the equation by -2

`(-2y)/(-2)=(-10)/(-2) -(-5x)/(-2)\\\\y=(-10)/(-2) +(-5x)/(-2) \\\\y=5+(5x)/(2)`

(negative+negative=positive)

re-write in slope-intercept form
`y=mx+b` , where m is the slope and b is the y-intercept

`y=(5)/(2)x+5`

Now you know that the slope is
`(5)/(2)x` and the y-intercept is
`5`.

Now, to graph, you just need to choose random values for x (like 0,1,2,3 or any other number) and insert into the equation
`y=(5)/(2)x+5` to find the points, or you can just use the slope. To find the x-intercept, do the following:

make y equal to 0

`0=(5)/(2)x+5`

Solve for x:

simplify
`(5)/(2)x`

`0=(5x)/(2) +5`

Subtract 5 from both sides

`0-5=(5x)/(2)+5-5\\ \\-5=(5x)/(2)`

Multiply both sides by 2

`2(-5)=2((5x)/(2))\\\\-10=5x`

Divide both sides by 5

`(-10)/(5)= (5x)/(5)\\\\-2=x`

Flip

`x=-2`

The x-intercept is -2.