Write the equation of the line that passes through the points left bracket, minus, 8, comma, minus, 9, right bracket(−8,−9) and left bracket, 3, comma, minus, 4, right bracket(3,−4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

To find the equation of the line, we can use the point-slope form of the equation.

The point-slope form is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope of the line.

First, let's find the slope (m) of the line using the two given points:

m = (y2 - y1) / (x2 - x1)

m = (-4 - (-9)) / (3 - (-8))
= (-4 + 9) / (3 + 8)
= 5 / 11

Now we can use the point (-8, -9) and the slope (5/11) to write the equation of the line in point-slope form:

y - (-9) = (5/11)(x - (-8))

Simplifying:

y + 9 = (5/11)(x + 8)

Rearranging the equation to fully simplified point-slope form:

y + 9 = (5/11)x + 40/11

So the equation of the line is:

y = (5/11)x + 40/11 - 9
or
y = (5/11)x + 40/11 - 99/11
or
y = (5/11)x - 59/11

Therefore, the equation of the line that passes through the points (-8, -9) and (3, -4) is y = (5/11)x - 59/11.