Question

What are the linear equations that could represent a line that goes through the point (-1, 5) and has a slope of -4/3?

a) y = -4/3x + 5
b) y = 4/3x + 5
c) y = -4x + 5
d) y = 4x + 5

Answer 1

None of the provided options correctly represents the line through the point (-1, 5) with a slope of -4/3. The correct equation of the line is y = -4/3x + 11/3.

Step-by-step explanation:

The student is asking for the linear equation that represents a line passing through the point (-1, 5) with a slope of -4/3. To find the equation of a line, we use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Using the given point to solve for b, we plug in the values: 5 = (-4/3)(-1) + b. This simplifies to 5 = 4/3 + b. Solving for b gives us b = 5 - 4/3 = 15/3 - 4/3 = 11/3. The correct equation is therefore y = -4/3x + 11/3, which matches none of the options provided.