Write the equation of the linear function that passes through the points (2,-2) and (-3,13)

Question

Y=__x +__

Answer 1

To find the equation of the linear function passing through the two points (2,-2) and (-3,13), first calculate the slope using the formula:

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

m = (13 - (-2)) / (-3 - 2)
m = (13 + 2) / (-5)
m = 15 / -5
m = -3

Using the slope-intercept form (y = mx + b) of the equation of a line, plug in the slope (-3) and one of the points (2, -2) to find the y-intercept (b):

-2 = -3(2) + b
-2 = -6 + b
b = -2 + 6
b = 4

Therefore, the equation of the linear function is:
Y = -3x + 4

Answer 2

That’s wrong

Answer 3

Apologies for the mistake. Let's recalculate the equation using the given points (2,-2) and (-3,13).

First, find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)
m = (13 - (-2)) / (-3 - 2)
m = (13 + 2) / (-5)
m = 15 / -5
m = -3

Next, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Using the point (2, -2):

y - (-2) = -3(x - 2)
y + 2 = -3x + 6
y = -3x + 4

Therefore, the correct equation of the linear function passing through the points (2,-2) and (-3,13) is:

Y = -3x + 4

Answer 4

Still wrong

Answer 5

Given points are (2,-2) and (-3,13).

Let's use the point-slope form of the equation of a line:

m = (13 - (-2)) / (-3 - 2)
m = 15 / -5
m = -3

Choose one of the points and substitute into the point-slope form:

y - y₁ = m(x - x₁)
y - (-2) = -3(x - 2)
y + 2 = -3(x - 2)
y + 2 = -3x + 6
y = -3x + 4

Therefore, the equation of the linear function passing through the points (2,-2) and (-3,13) is:

Y = -3x + 4