Questions: Find the slope of the line that passes through these two points. (5,5) ;(6,9) Simplify your answer completely. Slope =[?] Slope Formula: (y2-y1)/(x2-x1)

Transcript text: Find the slope of the line that passes through these two points. \[ (5,5) ;(6,9) \] Simplify your answer completely. \[ \text { Slope }=[?] \] Slope Formula: $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Solution

Solution Steps

To find the slope of the line passing through the points (5, 5) and (6, 9), we use the slope formula: \[ \text{Slope} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \] Here, $(x_1, y_1) = (5, 5)$ and $(x_2, y_2) = (6, 9)$. Substitute these values into the formula to calculate the slope.

Step 1: Identify the Points

We are given two points through which the line passes: $(x_1, y_1) = (5, 5)$ and $(x_2, y_2) = (6, 9)$.

Step 2: Apply the Slope Formula

Using the slope formula \[ \text{Slope} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}, \] we substitute the values: \[ \text{Slope} = \frac{9 - 5}{6 - 5} = \frac{4}{1} = 4.0. \]

Step 3: Simplify the Result

The slope simplifies to $4.0$, which can be expressed as $4$.