Question

In the linear function F

F(0)=2
F(-6)=0

What is the equation of F?

F(x)=
3
1
​
x−6

F(x)=
3
1
​
x+2

F(x)=3x−6

F(x)=3x+2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the linear function F, we need to find the slope (m) and the y-intercept (b) using the given information.

Since F(0) = 2, we know that the y-intercept is 2. Thus, b = 2.

To find the slope, we can use the two given points (0, 2) and (-6, 0).

The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (0, 2) and (-6, 0), we have:
m = (0 - 2) / (-6 - 0) = -2 / -6 = 1/3

So the slope is 1/3.

Therefore, the equation of F is:
F(x) = 1/3x + 2

Answer 2

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

To find the equation of the linear function, we need to determine the slope (m) and the y-intercept (b) using the given information.

First, let's find the slope (m):
The slope can be determined using the formula: m = (y2 - y1) / (x2 - x1)

Using the given points:
(x1, y1) = (0, 2)
(x2, y2) = (-6, 0)

m = (0 - 2) / (-6 - 0)
m = -2 / -6
m = 1/3

Now, let's find the y-intercept (b):
Using the point (0, 2) and the slope (m = 1/3), we can use the formula: y = mx + b

2 = (1/3)(0) + b
2 = 0 + b
b = 2

The equation of F is given by: F(x) = mx + b

Substituting m = 1/3 and b = 2:
F(x) = 1/3x + 2

Therefore, the correct equation of F is F(x) = 1/3x + 2.

Answer 3

[AI-generated answer — Explain Bot]

To find the equation of the linear function F, we can use the given information about the function's values at specific input values.

First, let's calculate the slope of the function. The slope of a linear function is equal to the change in the dependent variable (y-value) divided by the change in the independent variable (x-value). We can use the two points (0, 2) and (-6, 0) to calculate the slope.

slope = (change in y) / (change in x)
= (0 - 2) / (-6 - 0)
= -2 / -6
= 1/3

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of F. The point-slope form is given by:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Let's use the point (0, 2) to write the equation in point-slope form:

y - 2 = (1/3)(x - 0)
y - 2 = (1/3)x

To convert this equation to slope-intercept form (y = mx + b), we can simplify it:

y = (1/3)x + 2

Therefore, the equation of the linear function F is:

F(x) = (1/3)x + 2