Question

Use the image to answer the question. An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis. Derive the equation of the line in slope-intercept form.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form (y = mx + b), we first need to find the slope (m) and the y-intercept (b).

First, calculate the slope using the formula:

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

Substitute the coordinates of the two points into the formula:

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

Now that we have the slope, we can use one of the points and the slope to find the y-intercept (b). We can use the point (0,4) and substitute it into the slope-intercept form equation:

4 = 4(0) + b
4 = b

Now that we have the slope (m = 4) and the y-intercept (b = 4), we can write the equation in slope-intercept form:

y = 4x + 4

Answer 2

very loud incorrect buzzer sound

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the error. Let's correct that.

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

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

Taking the points (0, 4) and (1, 8):

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

So, the slope of the line is 4.

Next, we can find the y-intercept (b) by using the slope and one of the points. Using point (0, 4):

4 = 4(0) + b
b = 4

Now we have the slope (m = 4) and the y-intercept (b = 4), we can write the equation in slope-intercept form:

y = 4x + 4.

Answer 4

It's still wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's correct the calculation.

First, let's calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4

Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (0, 4) in the slope-intercept form equation:

4 = 4(0) + b
b = 4

Now substituting the slope and the y-intercept into the slope-intercept form equation, we get:

y = 4x + 4

Therefore, the equation of the line in slope-intercept form is y = 4x + 4. Thank you for your patience.

Answer 6

Bot it's wrong, change your answer.

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the errors in the previous responses. Let's correct that now.

Given the points (0, 4) and (1, 8), we will find the equation of the line passing through these points in slope-intercept form (y = mx + b).

First, let's calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4

Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (0, 4) in the slope-intercept form equation:

4 = 4(0) + b
4 = b

So far, we have found that the slope (m) is 4 and the y-intercept (b) is also 4.

The equation of the line in slope-intercept form is:

y = 4x + 4.

Thank you for your patience, and I appreciate your feedback.

Answer 8

It isn't 4x + 4

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let's correct it by finding the correct equation of the line in slope-intercept form.

Given the points (0, 4) and (1, 8), we found the slope (m) to be 4.

Now, to find the y-intercept, we can substitute one of the points into the equation:

Using the point (0, 4):
4 = 4(0) + b
4 = b

So, the y-intercept is 4.

Therefore, the equation of the line in slope-intercept form (y = mx + b) is:
y = 4x + 4

Thank you for your patience, and I appreciate your feedback.