Write an equation in slope-intercept form for the line through points (-2,6) and (7,-1).(1 point) Responses y = (7/9)x + 40/9 y = (7/9)x + 40/9 y = (7/9)x + 9/40 y = (7/9)x + 9/40 y = (-7/9)x + 9/40 y = (-7/9)x + 9/40 y = (-7/9)x + 40/9 y = (-7/9)x + 40/9

Answer 1

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

First, let's find the slope 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

Now let's find the y-intercept using the slope-intercept form:

y = mx + b

Substituting one of the points (7, -1) and the slope (-7/9):

-1 = (-7/9)(7) + b
-1 = (-49/9) + b

To find b, we can solve the equation above for b:

b = -1 + (49/9)
b = -9/9 + 49/9
b = 40/9

Therefore, the equation of the line is:

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