A coordinate plane with a straight line with a positive slope passing through the points, (0, negative 3) and (3, 4).

Choose the answer to complete each statement.

The slope of the line is
.

The y-intercept is at
.

The graph represents the function

1 answer

Let's analyze the given information to complete the statements.

1. **The slope of the line is:**
The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points \((0, -3)\) and \((3, 4)\):
\[ m = \frac{4 - (-3)}{3 - 0} = \frac{4 + 3}{3} = \frac{7}{3} \]

So, the slope of the line is **\( \frac{7}{3} \)**.

2. **The y-intercept is at:**
The y-intercept of a line is the value of \( y \) when \( x = 0 \). Given the point \((0, -3)\), the y-intercept is **-3**.

3. **The graph represents the function:**
The equation of a line in slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Substituting the slope \( \frac{7}{3} \) and y-intercept \(-3\):
\[ y = \frac{7}{3}x - 3 \]

So, the graph represents the function **\( y = \frac{7}{3}x - 3 \)**.

Therefore, the completed statements are:

- The slope of the line is **\( \frac{7}{3} \)**.
- The y-intercept is at **-3**.
- The graph represents the function **\( y = \frac{7}{3}x - 3 \)**.