Question

Convert the equation into slope intercept form. Then, state the slips and y intercepts (please explain!

3x - 6y = -18

Answer 1

slope-intercept form:
`\boxed{\sf y = (1)/(2) x + 3.}`

Slope (m):
`\sf (1)/(2)`

Y-intercept (b): 3

Explanation:

The equation you provided is in standard form: 3x - 6y = -18.

In order to convert it into
`\textsf{slope-intercept form :}\boxed{\sf y = mx + b}`,

where "m" is the slope and "b" is the y-intercept,

Follow this steps.

Start with the given equation:

`\sf 3x - 6y = -18.`

Subtract 3x from both sides of the equation:

`\sf -6y = -3x - 18.`

Divide both sides by -6:

`\sf (-6y)/(-6)=(-3)/(-6)-(18)/(-6)`

`\sf y = (1)/(2) x + 3.`

Now the equation is in slope-intercept form:
`\boxed{\sf y = (1)/(2) x + 3.}`

The slope (m) is the coefficient of the x-term, which is
`(1)/(2)`

This means that for every increase of 1 in the x-coordinate, the y-coordinate will increase by
`\sf (1)/(2)`

The slope indicates the rate of change of the y-coordinate with respect to the x-coordinate.

The y-intercept (b) is the constant term in the equation, which is 3.

It represents the point where the graph of the line crosses the y-axis.

In other words, when x = 0, y = 3.

To summarize:

slope-intercept form:
`\boxed{\sf y = (1)/(2) x + 3.}`

Slope (m):
`\sf (1)/(2)`

Y-intercept (b): 3