Question

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

Answer 1

The equation of the line passing through the points (-6,7), (-4,2), (-2,-3), and (0,-8) is
`\(y = -(5)/(2)x - 8\)`, expressed in fully simplified slope-intercept form.

To find the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we first need to calculate the slope using the given points.

`\[ \text{Slope (m)} = \frac{\text{change in } y}{\text{change in } x} \]`

Using the points (-6,7) and (0,-8):

`\[ m = (-8 - 7)/(0 - (-6)) = (-15)/(6) = -(5)/(2) \]`

Now, pick one of the points (let's use (-6,7)) and substitute it into the slope-intercept form to find b:

`\[ 7 = -(5)/(2)(-6) + b \]`

Solving for b:

`\[ 7 = 15 + b \]\[ b = -8 \]`

Therefore, the equation of the line is:

`\[ y = -(5)/(2)x - 8 \]`