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

Question

coordinates are (1, 8) and (0, 4) and the line passes through the four on the y-axis.

Answer 1

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:

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

Using the coordinates (1, 8) and (0, 4), we get:

m = (4 - 8) / (0 - 1)
m = (-4) / (-1)
m = 4

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Substituting the slope (m = 4) and the coordinates (0, 4), we get:

y - 4 = 4(x - 0)
y - 4 = 4x

To convert this equation to slope-intercept form (y = mx + b), we isolate y:

y = 4x + 4

Since the line passes through the point (0, 4), we substitute the x and y values into the final equation to find the y-intercept (b):

4 = 4(0) + b
4 = 0 + b
b = 4

Therefore, 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.

the coordinates are (0, 2) and (-1, 1) and the line passes through the 2 on the y-axis.

Answer 3

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:

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

Using the coordinates (0, 2) and (-1, 1), we get:

m = (1 - 2) / (-1 - 0)
m = -1 / -1
m = 1

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Substituting the slope (m = 1) and the coordinates (0, 2), we get:

y - 2 = 1(x - 0)
y - 2 = x

To convert this equation to slope-intercept form (y = mx + b), we isolate y:

y = x + 2

Since the line passes through the point (0, 2), we substitute the x and y values into the final equation to find the y-intercept (b):

2 = 1(0) + b
2 = 0 + b
b = 2

Therefore, the equation of the line in slope-intercept form is:

y = x + 2

Answer 4

thats wrong..

Answer 5

Apologies for the mistake. Let's correct it.

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:

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

Using the coordinates (0, 2) and (-1, 1), we get:

m = (1 - 2) / (-1 - 0)
m = -1 / -1
m = 1

Now that we have the slope, we can use the slope-intercept form of a linear equation: y = mx + b.

We are given that the line passes through the point (0, 2), which means the y-intercept (b) is 2.

Therefore, the equation of the line in slope-intercept form is:

y = 1x + 2
y = x + 2

Answer 6

that's still wrong. let me say the question again.

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

the coordinates are (0, 2) and (-1, 1) and the line passes through the 2 on the y-axis.

Answer 7

Apologies for the mistake. Let's correct it.

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:

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

Using the coordinates (0, 2) and (-1, 1), we get:

m = (1 - 2) / (-1 - 0)
m = -1 / -1
m = 1

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Substituting the slope (m = 1) and the coordinates (0, 2), we get:

y - 2 = 1(x - 0)
y - 2 = x

To convert this equation to slope-intercept form (y = mx + b), we isolate y:

y = x + 2

Since the line passes through the point (0, 2), we substitute the x and y values into the final equation to find the y-intercept (b):

2 = 0 + b
b = 2

Therefore, the equation of the line in slope-intercept form is:

y = x + 2

Answer 8

wait, that was actually *my* mistake, i was wrong. i'm sorry. okay, the coordinates are (0, 2) and (1, -1) and the line passes through the two on the y-axis.

Answer 9

No problem. Let's solve it with the correct information.

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:

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

Using the coordinates (0, 2) and (1, -1), we get:

m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Substituting the slope (m = -3) and the coordinates (0, 2), we get:

y - 2 = -3(x - 0)
y - 2 = -3x

To convert this equation to slope-intercept form (y = mx + b), we isolate y:

y = -3x + 2

Since the line passes through the point (0, 2), we substitute the x and y values into the final equation to find the y-intercept (b):

2 = -3(0) + b
2 = 0 + b
b = 2

Therefore, the equation of the line in slope-intercept form is:

y = -3x + 2

Answer 10

write the equation of the line in slope-intercept form. the coordinates are (3, 0) and (0, -2) and the line passes through the -2 on the y-axis.

Answer 11

To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:

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

Using the coordinates (3, 0) and (0, -2), we get:
m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Substituting the slope (m = 2/3) and the coordinates (3, 0), we get:
y - 0 = (2/3)(x - 3)
y = (2/3)(x - 3)

To convert this equation to slope-intercept form (y = mx + b), we simplify the equation:

y = (2/3)x - 6/3
y = (2/3)x - 2

Since the line passes through the point (0, -2), we substitute the x and y values into the final equation to find the y-intercept (b):

-2 = (2/3)(0) - 2
-2 = -2

Therefore, the equation of the line in slope-intercept form is:
y = (2/3)x - 2