Final answer:
The equation of the line with a slope of 4, passing through the point (-1, -4), is y = 4x. The y-intercept is found to be 0, resulting in the slope-intercept form without a constant term.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, which is y = mx + b, where 'm' represents the slope and 'b' represents the y-intercept, follow these steps:
- Start with the slope-intercept formula: y = mx + b.
- Insert the given slope (4) into the formula: y = 4x + b.
- Use the given point (-1, -4) to solve for 'b'. Plug in x = -1 and y = -4 into the equation: -4 = 4(-1) + b.
- Solve for 'b': -4 = -4 + b, so b = 0.
- The final equation of the line is y = 4x.
This line passes through the point (-1, -4) and has a slope of 4, which means for every increase of 1 on the horizontal axis, there is a rise of 4 on the vertical axis.