Question

Write an equation in point slope form for the line through the given point with the given slope , y=5/2x−10;(−6,−9).

a) y=−2/5x+14
b) y=5/2x+133/2
c) y=5/2x−14
d) y=2/5x−14

Answer 1

The point-slope form of the equation for the line passing through the point (-6, -9) with a slope of 5/2 is y = 5/2x + 6.

Step-by-step explanation:

To write the equation of a line in point-slope form, we use the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Given the point (-6, -9) and the slope 5/2, we can substitute these values into the formula to get y - (-9) = 5/2(x - (-6)). Simplifying this equation yields y + 9 = 5/2(x + 6). Further simplification gives us y + 9 = 5/2x + 15, and by subtracting 9 from both sides, we get the point-slope form: y = 5/2x + 6.