Question

Write the equation of a line passing through the points (5,-3) and (1,1) in point-slope form. I understand to do it the other way, but I need help with this one, please.

a) y + 3 = -1/4(x - 5)
b) y - 3 = -1/4(x - 5)
c) y - 1 = -1/4(x - 1)
d) y + 1 = -1/4(x - 1)

Answer 1

The equation of the line passing through the points (5,-3) and (1,1) in point-slope form, using the point (5, -3), is y + 3 = -1(x - 5).

Step-by-step explanation:

To write the equation of a line passing through the points (5,-3) and (1,1) in point-slope form, we need to find the slope of the line first. The slope, denoted as m, is calculated using the formula m = (y2 - y1) / (x2 - x1). From the provided points, using (5, -3) as (x1, y1) and (1, 1) as (x2, y2), we have:

• m = (1 - (-3)) / (1 - 5)
• m = (1 + 3) / (1 - 5)
• m = 4 / (-4)
• m = -1

Now, we use one of the given points along with the slope to express the equation in point-slope form, which is y - y1 = m(x - x1). We can use either point, but let's use (5, -3):

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

This gives us the point-slope form of the line. However, we made a computation error while finding the slope. The correct slope should be:

• m = 4 / (-4)
• m = -1

Therefore, our initial calculation of the slope as -1/4 was incorrect; it should be -1. This means the correct equation in point-slope form using the point (5, -3) is y + 3 = -1(x - 5), which corresponds to choice b.