Question

Write an equation in​ point-slope form for the given line.

(-2,4) and (2,3)

A. y-3=1/4(x-2)

B y-3=-1/4 (x-2)

C. y-2=1/4(x-3)

D. y-2=-1/4(x-3)

Answer 1

To write the equation in point-slope form, we need to use the formula:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Given the two points (-2,4) and (2,3), we can find the slope using the formula:

m = (y2 - y1)/(x2 - x1)

Plugging in the coordinates, we have:

m = (3 - 4)/(2 - (-2))

Simplifying, we get:

m = -1/4

Choosing one of the given points, for example (-2,4), we can write the equation using point-slope form:

y - y1 = m(x - x1)

y - 4 = (-1/4)(x - (-2))

Expanding the equation, we get:

y - 4 = (-1/4)(x + 2)

Finally, we can simplify the equation to:

y - 4 = (-1/4)x - 1/2

Adding 4 to both sides of the equation, we get:

y = (-1/4)x + 7/2

So the equation in point-slope form is:

B. y - 3 = -1/4(x - 2)