Derive the equation of the line in slope-intercept form.

Question

(1, 8), (0, 4)

Answer 1

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

Answer 2

write the equation of the line in slope-intercept form.
(0, 2), (1, -1)

Answer 3

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

Answer 4

write the equation of the line in slope-intercept form.
(3, 0), (0,-2)

Answer 5

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

Answer 6

Derive the equation of the line in slope-intercept form.
(1, -1), (0, -4)

Answer 7

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

Answer 8

write the equation of the line in slope-intercept form.
(0, 1), (1, -4)

Answer 9

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

Answer 10

use the table to answer the question.
x= -2, 0, 2
y= -1, 1, 3

write an equation that represents this nonproportional linear relationship.

Answer 11

To find the equation of the line representing the non-proportional linear relationship between the given points, we can first calculate the slope using two of the points:

Slope (m) = (y2 - y1) / (x2 - x1)

Choosing the points (-2, -1) and (2, 3):
m = (3 - (-1)) / (2 - (-2))
m = (3 + 1) / 4
m = 4 / 4
m = 1

Now that we have the slope (m = 1), we can use the point-slope form of a linear equation: y - y1 = m(x - x1)

Choosing the point (0, 1) to substitute:
y - 1 = 1(x - 0)
y - 1 = x
y = x + 1

Therefore, the equation that represents the non-proportional linear relationship between the given points is y = x + 1.