Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

`\sf y = -(5)/(6)x - 1`

Explanation:

To find the equation of a line. let's take two points (-6,4) and (6,-6)

When two points are given:

`\sf (x_1, y_1)` and
`\sf (x_2, y_2)`, we can use the slope-intercept form:

`\sf y = mx + b`

where
`\sf m` is the slope and
`\sf b` is the y-intercept. The slope
`\sf m` is given by:

`\sf m = \frac{{y_2 - y_1}}{{x_2 - x_1}}`

Let's use the points
`\sf (-6, 4)` and
`\sf (6, -6)` to find the slope:

`\sf m = \frac{{-6 - 4}}{{6 - (-6)}}`

`\sf m = \frac{{-10}}{{12}}`

`\sf m = -(5)/(6)`

Now that we have the slope
`\sf m`, let's use one of the points (let's use
`\sf (-6, 4)`) to find the y-intercept
`\sf b`:

`\sf 4 = (-(5)/(6))(-6) + b`

`\sf 4 = 5 + b`

`\sf b = 4-5`

`\sf b = -1`

Now that we have the slope
`\sf m = -(5)/(6)` and the y-intercept
`\sf b = -1`, we can write the equation of the line in slope-intercept form:

`\sf y = -(5)/(6)x - 1`

So, the equation of the line in fully simplified slope-intercept form is:

`\sf y = -(5)/(6)x - 1`