Write the equation of the linear function that passes through the points ( 3,−7) and ( −2, 6).

Answer 1

First, let's find the slope of the line using the formula:

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

m = (6 - (-7))/(-2 - 3)

m = (6 + 7)/(-5)

m = 13/-5

m = -13/5

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

y - y1 = m(x - x1)

Using the point (3, -7):

y - (-7) = -13/5(x - 3)

y + 7 = -13/5(x - 3)

y + 7 = -13/5x + 39/5

y = -13/5x + 39/5 - 7

y = -13/5x + 39/5 - 35/5

y = -13/5x + 4/5

Therefore, the equation of the linear function passing through the points (3, -7) and (-2, 6) is y = -13/5x + 4/5.