Question

Write an equation in slope intercept form of the line that passes through the given point and has the given point

Answer 1

The equation of the line passing through the point (-8, -2) with a slope of
`\(-(3)/(4)\)` in slope-intercept form is
`\(y = -(3)/(4)x - 8\).`

To write the equation of a line in slope-intercept form (y = mx + b), you can substitute the given values into the formula, where m is the slope and (x, y) are the coordinates of a point on the line.

Given point: (-8, -2)

Slope (m):
`\(-(3)/(4)\)`

Substitute into the slope-intercept form:

y = mx + b

`\[ -2 = \left(-(3)/(4)\right)(-8) + b \]`

Simplify:

-2 = 6 + b

Now, solve for b:

b = -2 - 6 = -8

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

`\[ y = -(3)/(4)x - 8 \]`