For each exercise below, find the equation of the line passing through the given points. Circle the two letters next to the correct equation. Then write these letters in the two boxes at the bottom of the page that contain the number of that exercise
(3, -1) and (-6, -4)
To find the equation of the line passing through the points (3, -1) and (-6, -4), we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
1. Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (-4 - (-1)) / (-6 - 3)
m = (-4 + 1) / (-6 - 3)
m = -3 / -9
m = 1/3
2. Plug in the values of the slope (1/3) and one of the points (3, -1) into the slope-intercept form y = mx + b to find the y-intercept (b):
-1 = (1/3)(3) + b
-1 = 1 + b
b = -2
3. The equation of the line is y = (1/3)x - 2.
Now, let's look at the given equations and circle the correct one:
a) y = 1/3x + 2
b) y = 1/3x - 2
c) y = 3x - 2
d) y = -3x - 2
The correct equation is b) y = 1/3x - 2.
Now, we write the letters in the two boxes at the bottom of the page:
Letter 1: b
Letter 2: (none)