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
(-1, -4) (2, 0)
To find the equation of the line passing through two points, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where (x1, y1) are the coordinates of one of the points and m is the slope of the line.
Given the points (-1, -4) and (2, 0), we can find the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the points:
m = (0 - (-4)) / (2 - (-1))
= 4 / 3
Now, we can use one of the points and the slope to find the equation of the line.
Let's use the point (-1, -4):
y - (-4) = (4/3)(x - (-1))
y + 4 = (4/3)(x + 1)
Now, let's rearrange the equation to get it in slope-intercept form (y = mx + b):
y + 4 = (4/3)x + 4/3
y = (4/3)x + 4/3 - 12/3
y = (4/3)x - 8/3
The equation of the line passing through the points (-1, -4) and (2, 0) is:
y = (4/3)x - 8/3
Next, we need to circle the two letters next to the correct equation. Since the equation we found is in slope-intercept form (y = mx + b), we need to look for the letters next to an equation in this form. Let's say the options are:
A) y = 3x + 2
B) y = (4/3)x - 8/3
C) y = -2x + 5
D) y = (3/4)x + 2
From the options, we can see that the correct equation is B) y = (4/3)x - 8/3.
Writing the letters in the boxes, the answer would be B) y = (4/3)x - 8/3.