To derive the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) using the points given.
The two points provided are:
- (0, -4)
- (1, -1)
Step 1: Calculate the slope (m)
The formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂) is: \[ m = \frac{y₂ - y₁}{x₂ - x₁} \]
Using our points:
- (x₁, y₁) = (0, -4)
- (x₂, y₂) = (1, -1)
Now plug in the values: \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]
Step 2: Use the slope to find the y-intercept (b)
We can use one of the points to find b. We can use (0, -4): The equation of the line in slope-intercept form is: \[ y = mx + b \]
Substituting m and the point (0, -4): \[ -4 = 3(0) + b \implies -4 = b \]
So the y-intercept (b) is -4.
Step 3: Write the equation
Now we substitute m and b back into the slope-intercept form: \[ y = 3x - 4 \]
Thus, the equation of the line in slope-intercept form is: \[ y = 3x - 4 \]
The correct response is: y = 3x - 4.