The linear function y=g(x) is graphed in the xy-plane. IF g(-3)=4 and g(2)=19, what is the slope of line g?

Answer

To find the slope of the linear function \( g(x) \), we can use the formula for the slope between two points on a line. The slope \( m \) is calculated as follows:

### Step 1: Identify the points
We are given two points based on the function values:
- Point 1: \( (-3, 4) \) where \( g(-3) = 4 \)
- Point 2: \( (2, 19) \) where \( g(2) = 19 \)

### Step 2: Use the slope formula
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
In our case:
- \( x_1 = -3 \), \( y_1 = 4 \)
- \( x_2 = 2 \), \( y_2 = 19 \)

### Step 3: Substitute the values into the formula
Substituting the values into the slope formula:
\[ m = \frac{19 - 4}{2 - (-3)} \]

### Step 4: Simplify the numerator and denominator
Calculating the numerator:
\[ 19 - 4 = 15 \]
Calculating the denominator:
\[ 2 - (-3) = 2 + 3 = 5 \]

### Step 5: Calculate the slope
Now substituting back into the slope formula:
\[ m = \frac{15}{5} = 3 \]

### Conclusion
The slope of the line \( g \) is \( 3 \).

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