Question

Write an equation in slope-intercept form for the line through points (-2,6) and (7,-1).(1 point)

Responses

y = (7/9)x + 9/40
y = (7/9)x + 9/40

y = (7/9)x + 40/9
y = (7/9)x + 40/9

y = (-7/9)x + 40/9
y = (-7/9)x + 40/9

y = (-7/9)x + 9/40

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of a line in slope-intercept form, use the formula y = mx + b, where m is the slope and b is the y-intercept.

First, find the slope of the line using the formula:

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

Using the points (-2, 6) and (7, -1):

m = (-1 - 6) / (7 - (-2))
m = (-7) / (7 + 2)
m = -7 / 9

So, the slope of the line is -7/9.

To find the y-intercept, substitute one of the points into the equation and solve for b. Using the point (-2, 6):

6 = (-7/9)(-2) + b
6 = 14/9 + b
6 - 14/9 = b
54/9 - 14/9 = b
40/9 = b

So, the y-intercept is 40/9.

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

y = (-7/9)x + 40/9

Therefore, the correct answer is:

y = (-7/9)x + 40/9

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the equation of the line in slope-intercept form (y = mx + b), first calculate the slope (m) using the formula:

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

Substitute the values of the two points (-2, 6) and (7, -1) into the formula:

m = (-1 - 6) / (7 - (-2))
m = (-7) / (9)
m = -7/9

Now that we have the slope (m), we can use one of the given points and the slope in the equation y = mx + b to solve for the y-intercept (b). Let's use the point (-2, 6):

6 = (-7/9)(-2) + b
6 = 14/9 + b

To solve for b, subtract 14/9 from both sides:

6 - 14/9 = b
54/9 - 14/9 = b
40/9 = b

So the y-intercept (b) is 40/9.

Now we have the slope (m = -7/9) and the y-intercept (b = 40/9), we can write the equation in slope-intercept form:

y = (-7/9)x + 40/9

Therefore, the correct equation in slope-intercept form for the line through the points (-2, 6) and (7, -1) is y = (-7/9)x + 40/9.

Answer 3

[AI-generated answer — Explain Bot]

To find the equation of a line in slope-intercept form, we need to use the formula:

y = mx + b

where m represents the slope of the line and b represents the y-intercept.

To find the slope (m), we can use the formula:

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

Using the given points, (-2,6) and (7,-1), we can substitute the coordinates into the formula:

m = (-1 - 6) / (7 - (-2))
= (-7) / (9)
= -7/9

Now that we have the slope, we can substitute it into the slope-intercept form equation:

y = (-7/9)x + b

To find the y-intercept (b), we can use one of the given points. Let's use the point (-2,6):

6 = (-7/9)(-2) + b
6 = 14/9 + b
6 - 14/9 = b
54/9 - 14/9 = b
40/9 = b

Now we have the value of b. The final equation in slope-intercept form for the line through points (-2,6) and (7,-1) is:

y = (-7/9)x + 40/9