To write the equation of a line in slope-intercept form, which is given by the equation \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), we first need to determine the slope and the y-intercept based on the description.
From your description:
- The line starts at \( (40, 0) \) on the x-axis (this is where the line crosses the x-axis).
- It stretches diagonally downward as it moves toward the bottom left.
Since it is moving downwards and to the left, the slope will be negative.
Step 1: Determine Two Points on the Line
We already know one point on the line, \( (40, 0) \). Now, we need another point. You mentioned it stretches down to -20 on the y-axis, which implies that the line crosses the y-axis at \( (0, -20) \).
So, we have two points:
- \( (40, 0) \)
- \( (0, -20) \)
Step 2: Calculate the Slope
The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (40, 0) \) and \( (0, -20) \):
\[ m = \frac{-20 - 0}{0 - 40} = \frac{-20}{-40} = \frac{1}{2} \]
Step 3: Determine the y-Intercept
From the second point \( (0, -20) \), we see that the y-intercept \( b \) is -20.
Step 4: Write the Equation
Now that we have both the slope \( m = \frac{1}{2} \) and the y-intercept \( b = -20 \), we can write the equation of the line in slope-intercept form:
\[ y = \frac{1}{2}x - 20 \]
Thus, the final equation of the line in slope-intercept form is:
\[ y = \frac{1}{2}x - 20 \]