Question

What is the equation of a line, in point- slope form, that passes through (5, –3)and has a slope of 2/3?

A. y+3= 2/3 (x-5)
B. y+5= 2/3 (x-3)
C. y-3= 2/3 (x+5)
D. y-5= 2/3 (x+3)

Answer 1

The correct equation of a line in point-slope form that passes through the point (5, –3) with a slope of 2/3 is y + 3 = 2/3 (x - 5), which is option A.

Step-by-step explanation:

The equation of a line in point-slope form that passes through a specific point (x1, y1) with a given slope m is written as:

y - y1 = m(x - x1)

To solve for the equation passing through the point (5, –3) with a slope of 2/3, we plug these values into the point-slope formula:

y - (-3) = (2/3)(x - 5)

Remember to handle the negative sign carefully, resulting in:

y + 3 = (2/3)(x - 5)

Therefore, the correct equation in point-slope form is option A: y + 3 = 2/3 (x - 5).