This graph shows a linear function whose domain is the set of integers.

Question

the main points are (3,4)(6,3)
Write an equation for the function in the form f(x)=mx+b.
f(x)=

Answer 1

To find the equation of the linear function in the form $f(x)=mx+b$, we first need to determine the slope $m$ using the two given points: $(3,4)$ and $(6,3)$.

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Plugging in the coordinates of the points:

• $(x_1,y_1)=(3,4)$
• $(x_2,y_2)=(6,3)$

$$m=\frac{3-4}{6-3}=\frac{-1}{3}=-\frac{1}{3}$$

Now we have the slope $m=-\frac{1}{3}$.

Next, we use the point-slope form of a linear equation, which is:

$$y-y_1=m(x-x_1)$$

We can use one of the points, for example $(3,4)$:

$$y-4=-\frac{1}{3}(x-3)$$

Now we simplify this equation to the slope-intercept form $y=mx+b$:

1. Distribute $-\frac{1}{3}$:

$$y-4=-\frac{1}{3}x+1$$

2. Add 4 to both sides:

$$y=-\frac{1}{3}x+1+4$$ $$y=-\frac{1}{3}x+5$$

Thus, the equation of the function is:

$$f(x)=-\frac{1}{3}x+5$$