Question

What is the equation in point-slope form for the line that passes through the points (-3,5) and (2,-3)?

1) y - 3 = -5/8(x + 5)
2) y - 3 = -8/5(x + 5)
3) y - 5 = -8/5(x + 3)
4) y - 5 = 8/5(x + 3)

Answer 1

The equation in point-slope form for the line passing through the points (-3,5) and (2,-3) is y - 5 = -8/5(x + 3).

Step-by-step explanation:

To find the equation of a line in point-slope form, we need to use the formula:

y - y1 = m(x - x1)

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

Given the points (-3,5) and (2,-3), we can calculate the slope using the formula:

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

Substituting the values into the formula, we get:

m = (-3 - 5) / (2 - (-3)) = -8 / 5

Now, we can use one of the given options to substitute the values and check which equation is correct. Let's go through the options:

1. y - 3 = -5/8(x + 5)
2. y - 3 = -8/5(x + 5)
3. y - 5 = -8/5(x + 3)
4. y - 5 = 8/5(x + 3)

Substituting the point (-3,5) into each equation, we find that option 3) y - 5 = -8/5(x + 3) is the correct equation in point-slope form for the line that passes through the given points.