To determine the slope and y-intercept of the line based on the provided points, we can start by selecting two points to calculate the slope.
Step 1: Calculate the Slope (m)
Using the points (-2, 80) and (5, 10):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (-2, 80)\) and \((x_2, y_2) = (5, 10)\).
\[ m = \frac{10 - 80}{5 - (-2)} = \frac{-70}{7} = -10 \]
Step 2: Calculate the Y-Intercept (b)
Using the slope \(m = -10\) and one of the given points. We'll use the point \((5, 10)\):
The equation of the line in the slope-intercept form is:
\[ y = mx + b \]
Substituting in the values we know:
\[ 10 = -10(5) + b \]
\[ 10 = -50 + b \]
\[ b = 10 + 50 = 60 \]
Step 3: Write the Equation of the Line
Now, we can write the equation of the line:
\[ y = -10x + 60 \]
Summary of Results
- Slope of the line: \( -10 \)
- Y-intercept of the line: \( 60 \)
- Equation of the line: \( y = -10x + 60 \)
Therefore, the correct responses are:
- Slope: -10
- Y-intercept: 60
- Equation of the line: \( y = -10x + 60 \)