To determine the function rule in slope-intercept form, we need to find the slope [tex]\( m \)[/tex] and y-intercept [tex]\( b \)[/tex] of the line that passes through the given points on the graph.
Let's consider the points [tex]\( (0, 3) \)[/tex] and [tex]\( (2, 7) \)[/tex].
### Step 1: Calculate the Slope [tex]\( m \)[/tex]
The slope formula is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given points:
[tex]\[
m = \frac{7 - 3}{2 - 0} = \frac{4}{2} = 2.0
\][/tex]
### Step 2: Calculate the Y-intercept [tex]\( b \)[/tex]
The slope-intercept form of a line is:
[tex]\[
y = mx + b
\][/tex]
Given one of the points, let's use [tex]\( (0, 3) \)[/tex]:
[tex]\[
3 = 2.0 \cdot 0 + b \implies b = 3.0
\][/tex]
### Step 3: Form the Equation
Finally, substituting the values of [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the slope-intercept form:
[tex]\[
f(x) = 2.0x + 3.0
\][/tex]
Thus, the function rule in slope-intercept form is:
[tex]\[
f(x) = 2.0x + 3.0
\][/tex]
