Final answer:
The equation of a line passing through the point (2, −7) with a slope of −4 is found using the slope-intercept form. After plugging the slope and the point into the equation, solving for the y-intercept gives us the final equation: y = −4x + 1.
Step-by-step explanation:
To find the equation of a line that passes through the point (2, −7) and has a slope of −4, we use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. Given the slope m = −4, we can substitute the point (2, −7) into the equation and solve for b.
- Start with the slope-intercept form: y = −4x + b.
- Substitute the given point into the equation: −7 = −4(2) + b.
- Simplify and solve for b: −7 = −8 + b, which gives b = 1.
- Write the final equation: y = −4x + 1.
This result indicates that the equation of the line that passes through the point (2, −7) with a slope of −4 is y = −4x + 1.