Question

Put the following equation of a line into slope-intercept form, simplifying all

fractions.
5x – 4y = -4

Answer 1

4y=5x+4
Divid by 4 to make slop intercept form
Y=5/4y +1
Slop =5/4

Answer 2

`\boxed {\boxed {\sf y= (5)/(4)x+1}}`

Explanation:

We are given the equation of a line and asked to put it into slope-intercept form.

Slope-intercept form is:

`y=mx+b`

Where:

• m= slope
• b= y-intercept

In order to put the equation into slope-intercept form, we have to isolate the variable y by performing the inverse operation.

`5x-4y= -4`

5x is being added to -4y. The inverse of addition is subtraction, so subtract 5x from both sides of the equation.

`5x-5x-4y=-4-5x`

`-4y=-4-5x`

The variable y is being multiplied by -4. The inverse of multiplication is division. Divide both sides of the equation by -4.

`\frac {-4y}{-4}=(-4-5x)/(-4)`

`y= (-4)/(-4)+(-5x)/(-4)`

`y=1+(5)/(4)x`

Rearrange the equation.

`y= (5)/(4)x+1`

The fractions are completely simplified, so this is our final answer.

The equation of the line in slope-intercept form is
`\bold {y= (5)/(4)x+1}}`.

The slope is 5/4 and the y-intercept is 1.