Question

Write the equation of the line that passes through the points (3, -4) and (-5, 3). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

a) y = -1/2x - 5/2
b) y = 1/2x + 5/2
c) y = -1/2x + 5/2
d) y = 1/2x - 5/2

Answer 1

To find the equation of the line passing through the points (3, -4) and (-5, 3), we use the point-slope form of a linear equation. The equation of the line is y + 4 = (-7/8)(x - 3).

Step-by-step explanation:

To find the equation of the line passing through the points (3, -4) and (-5, 3), we can use the point-slope form of a linear equation. The formula is: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope of the line.

1. Step 1: Calculate the slope (m) using the formula: m = (y2 - y1)/(x2 - x1). Plugging in the values, we get m = (3 - (-4))/(-5 - 3) = 7/-8 = -7/8.
2. Step 2: Choose one of the given points, let's say (3, -4), and substitute the values into the point-slope form: y - (-4) = (-7/8)(x - 3).
3. Step 3: Simplify the equation to fully reduced point-slope form: y + 4 = (-7/8)(x - 3).

So, the equation of the line passing through the given points is

y + 4 = (-7/8)(x - 3)