Question

What is the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4)?

a. y−4=−119(x+8)
b. y+4=−51(x−8)
c. y+4=−119(x−8)
d. y−4=−51(x+8)

Answer 1

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

Step-by-step explanation:

To find the equation of a line in point-slope form, we need to determine the slope of the line and one point on the line. Using the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two points, we can calculate the slope to be:

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

Next, we can use the point-slope form equation:

y - y1 = m(x - x1)

Plugging in the values of one of the given points, say (3, -5):

y - (-5) = 9 / -11(x - 3)

Simplifying:

y + 5 = -9/11(x - 3)

So, the equation in point-slope form of the line that passes through the points (3, -5) and (-8, 4) is y + 5 = -9/11(x - 3). Therefore, the correct answer is (b) y+4=−51(x−8).