Question

What is the point slope form of the line with slope 25 that passes through the point (−4, −7)?

(A) y+7=25(x+4)

​(B) y+4=25(x+7)​

(C) y−7=25(x−4)

(D) y−4=25(x−7)

Answer 1

Option A:
`y+7 = 25(x+4)` is the correct answer.

Explanation:

The point-slope form of an equation of a line is given by:

`y-y_1 = m(x-x_1)`

Here:

m is the slope of the line

`(x_1,y_1)` are the coordinates of the point from which the line passes.

Now looking at the given question:

`m = 25\\(x_1,y_1) = (-4,-7)`

Putting the values in the general form of point-slope form of equation of line

`y-(-7) = 25\{x-(-4)\}\\y+7 = 25(x+4)`

Hence, the point-slope form of given line is:

`y+7 = 25(x+4)`

Observing the option given, it can be concluded that Option A:
`y+7 = 25(x+4)` is the correct answer.