Question

What is the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4) ? Responses y+4=−911(x−8) y plus 4 equals negative fracion 9 over 11 end fraction open parenthesis x minus 8 close parenthesis y−4=−15(x+8) y minus 4 equals negative fraction 1 over 5 end fraction open parenthesis x plus 8 close parenthesis y−4=−911(x+8) y minus 4 equals negative fraction 9 over 11 end fraction open parenthesis x plus 8 close parenthesis y+4=−15(x−8)

Answer 1

The point-slope form of a line that passes through the points (3, −5) and (−8, 4) is y - 4 = -9/11(x + 8).

Step-by-step explanation:

To find the equation of a line in point-slope form that passes through two given points, we need to follow these steps:

1. Calculate the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1).
2. Choose one of the given points to use in the point-slope formula.
3. Plug in the values of the slope and the chosen point into the point-slope formula, which is y - y1 = m(x - x1), where (x1, y1) is the chosen point.

For the points (3, -5) and (-8, 4), we calculate the slope as follows:

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

Using the point (-8, 4), the point-slope form of the equation is:

y - 4 = (-9/11)(x + 8)

Here is the correct point-slope form equation derived from the given points.