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
(4, 1) and (-4, 7)
To find the equation of the line passing through the given points (4, 1) and (-4, 7), we can use the slope-intercept form of a line which is given by:
y = mx + b
where m represents the slope of the line and b represents the y-intercept.
Step 1: Find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates (4, 1) and (-4, 7) into the formula:
m = (7 - 1) / (-4 - 4)
m = 6 / (-8)
m = -3/4
Step 2: Substitute one of the points (4, 1) into the slope-intercept form to find the y-intercept (b):
1 = (-3/4)(4) + b
1 = -3 + b
b = 4
Step 3: Write the equation of the line using the slope (m) and y-intercept (b):
y = (-3/4)x + 4
Now we have the equation of the line passing through the given points.
The correct equation for this exercise is y = (-3/4)x + 4, so the two letters to circle are C and E.
C, E