Question

Give the equation of the line through the point ( – 9,5) with a slope of - 7/3 in slop-intercept form

a. y = (-7/3)x - 2
b. y = (-7/3)x - 5
c. y = (-6/3)x - 2

Answer 1

The correct equation of the line passing through (-9,5) with a slope of -7/3 is y = (-7/3)x - 16. The process involves plugging the given point and slope into the slope-intercept form and solving for the y-intercept, which in this case is -16. None of the provided options are correct.

Step-by-step explanation:

The student asked for the equation of the line through the point (-9, 5) with a slope of -7/3 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To find the y-intercept, we can use the given point and the slope to plug into the slope-intercept equation. Here are the steps:

1. Start with the formula y = mx + b.
2. Plug in the given point (-9, 5) and the slope (-7/3): 5 = (-7/3)(-9) + b.
3. Simplify: 5 = 21 + b.
4. Subtract 21 from both sides to solve for b: b = 5 - 21.
5. b = -16.

Now, we have m = -7/3 and b = -16, so the equation of the line is y = (-7/3)x - 16, which means none of the given options are correct. The correct equation is y = (-7/3)x - 16.