Question

What is the equation of the line that passes through the (2,−7) and has a slope of −4

Answer 1

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.

1. Start with the slope-intercept form: y = −4x + b.
2. Substitute the given point into the equation: −7 = −4(2) + b.
3. Simplify and solve for b: −7 = −8 + b, which gives b = 1.
4. 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.