Derive the equation of the line in slope-intercept form.
(1, 8), (0, 4)
To derive the equation of the line in slope-intercept form, we need to find the slope first.
The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is:
slope (m) = (y2 - y1) / (x2 - x1)
Given the points (1, 8) and (0, 4), we can substitute the values into the formula:
m = (4 - 8) / (0 - 1)
m = (-4) / (-1)
m = 4
Now that we have the slope (m = 4), we can use the slope-intercept form of a linear equation: y = mx + b
Substitute the slope (m = 4) and one of the points (0, 4) into the equation to solve for the y-intercept (b):
4 = 4(0) + b
4 = b
Now we have the slope (m = 4) and the y-intercept (b = 4), so the equation of the line in slope-intercept form is:
y = 4x + 4
write the equation of the line in slope-intercept form.
(0, 2), (1, -1)
To derive the equation of the line in slope-intercept form, we first need to calculate the slope using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Given the points (0, 2) and (1, -1), we can substitute the values into the formula:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now that we have the slope (m = -3), we can use the slope-intercept form of a linear equation: y = mx + b
Substitute the slope (m = -3) and one of the points (0, 2) into the equation to solve for the y-intercept (b):
2 = -3(0) + b
2 = b
Now we have the slope (m = -3) and the y-intercept (b = 2), so the equation of the line in slope-intercept form is:
y = -3x + 2
write the equation of the line in slope-intercept form.
(3, 0), (0,-2)
To derive the equation of the line in slope-intercept form, we first need to calculate the slope using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Given the points (3, 0) and (0, -2), we can substitute the values into the formula:
m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3
Now that we have the slope (m = 2/3), we can use the slope-intercept form of a linear equation: y = mx + b
Substitute the slope (m = 2/3) and one of the points (3, 0) into the equation to solve for the y-intercept (b):
0 = (2/3)(3) + b
0 = 2 + b
b = -2
Now we have the slope (m = 2/3) and the y-intercept (b = -2), so the equation of the line in slope-intercept form is:
y = (2/3)x - 2
Derive the equation of the line in slope-intercept form.
(1, -1), (0, -4)
To derive the equation of the line in slope-intercept form, we first need to calculate the slope using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Given the points (1, -1) and (0, -4), we can substitute the values into the formula:
m = (-4 - (-1)) / (0 - 1)
m = (-4 + 1) / -1
m = -3 / -1
m = 3
Now that we have the slope (m = 3), we can use the slope-intercept form of a linear equation: y = mx + b
Substitute the slope (m = 3) and one of the points (1, -1) into the equation to solve for the y-intercept (b):
-1 = 3(1) + b
-1 = 3 + b
b = -4
Now we have the slope (m = 3) and the y-intercept (b = -4), so the equation of the line in slope-intercept form is:
y = 3x - 4
write the equation of the line in slope-intercept form.
(0, 1), (1, -4)
To derive the equation of the line in slope-intercept form, we first need to calculate the slope using the formula:
slope (m) = (y2 - y1) / (x2 - x1)
Given the points (0, 1) and (1, -4), we can substitute the values into the formula:
m = (-4 - 1) / (1 - 0)
m = -5 / 1
m = -5
Now that we have the slope (m = -5), we can use the slope-intercept form of a linear equation: y = mx + b
Substitute the slope (m = -5) and one of the points (0, 1) into the equation to solve for the y-intercept (b):
1 = -5(0) + b
1 = b
Now we have the slope (m = -5) and the y-intercept (b = 1), so the equation of the line in slope-intercept form is:
y = -5x + 1
use the table to answer the question.
x= -2, 0, 2
y= -1, 1, 3
write an equation that represents this nonproportional linear relationship.