Question

Write the equation of the line that passes through the points (−9,−9) and (6,−7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

`\boxed{\sf y + 9 = (2)/(15)(x + 9) }`

Explanation:

To find the equation of the line that passes through the points (-9, -9) and (6, -7), we can use the point-slope form of the equation of a line:

`\boxed{\boxed{\sf y - y_1 = m(x - x_1) }}`

Where:

• m is the slope of the line.
• 
  `\sf (x_1, y_1)` is one of the given points on the line.,,

Let's use the point (-9, -9) as
`\sf (x_1, y_1)` and find the slope m using the second point (6, -7):

`\sf m = (y_2 - y_1)/(x_2 - x_1) \\\\ = ((-7) - (-9))/(6 - (-9))\\\\ = (-7 + 9)/(6 + 9) \\\\ = (2)/(15)`

Now that we have the slope, we can substitute it and one of the points (-9, -9) into the point-slope form:

`\sf y - (-9) = (2)/(15)(x - (-9))`

Simplify:

`\sf y + 9 = (2)/(15)(x + 9)`

Now, we can simplify it further, if needed, but this is the equation of the line in point-slope form:

`\boxed{\sf y + 9 = (2)/(15)(x + 9) }`