Question

Find the y-intercept of the line represented by the equation: -5x+3y=30

Answer 1

We need to find the y-intercept of the equation.

For this, we need to use the slope-intercept form:

`y=mx+b`

Where m represents the slope and b the y-intercept.

Now, to get the form, we need to solve the equation for y:

Then:

`-5x+3y=30`

Solving for y:

Add both sides 5x:

`-5x+5x+3y=30+5x`
`3y=30+5x`

Divide both sides by 3

`(3y)/(3)=(30+5x)/(3)`
`(3y)/(3)=(30)/(3)+(5x)/(3)`
`y=10+(5)/(3)x`

We can rewrite the expression as:

`y=(5)/(3)x+10`

Where 5/3x represents the slope and 10 represents the y-intercept.

The y-intercept represents when the graph of the equations intersects with the y-axis, therefore, it can be written as the ordered pair (0,10).