Write an equation in slope-intercept form for the line passing through (2,1) and (−1,−8).
A.
image
B.
image
C.
image
D.
image
The equation in slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept. To find the slope, we can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Let's use the points (2,1) and (-1,-8) to find the slope:
m = (-8 - 1) / (-1 - 2) = (-9) / (-3) = 3
Now that we have the slope, we can substitute it along with one of the given points (2,1) into the slope-intercept form equation to solve for the y-intercept (b):
1 = 3(2) + b
1 = 6 + b
b = 1 - 6
b = -5
Therefore, the equation in slope-intercept form for the line passing through (2,1) and (-1,-8) is y = 3x - 5.
So, the correct answer is D. image
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).
The formula for the slope, m, is given by:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Given the points (2,1) and (-1,-8), we can substitute the coordinates into the slope formula:
m = (-8 - 1) / (-1 - 2) = -9 / -3 = 3.
Now, we have the slope, m = 3.
Next, we can substitute one of the points, (2,1), into the slope-intercept form equation (y = mx + b) to solve for the y-intercept (b):
1 = 3(2) + b,
1 = 6 + b,
b = 1 - 6,
b = -5.
Therefore, the equation in slope-intercept form for the line passing through (2,1) and (-1,-8) is:
y = 3x - 5.
The correct answer is:
C. y = 3x - 5.
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the values of the slope (m) and the y-intercept (b).
Step 1: Find the slope (m)
The formula for finding the slope (m) of a line passing through two points, (x₁, y₁) and (x₂, y₂), is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Given the points (2,1) and (-1,-8), we can calculate the slope as follows:
m = (-8 - 1) / (-1 - 2)
m = (-9) / (-3)
m = 3
Step 2: Find the y-intercept (b)
To find the y-intercept (b), we can use any of the given points and substitute the values into the equation y = mx + b. Let's use the point (2,1):
1 = 3(2) + b
1 = 6 + b
b = 1 - 6
b = -5
Therefore, the equation of the line passing through (2,1) and (-1,-8) in slope-intercept form is:
y = 3x - 5
The correct answer is C. image