Question

A line passes through the point (–7, 5) and has a slope of 1/2. Which is another point that the line passes through?

(–13, 9)
(–9, 13)
(9, 13)
(13, 9)

Answer 1

Option C is correct.

Another point is, (9, 13)

Explanation:

Point slope form states the equation of a straight line in the form
`y-y_1=m(x-x_1)`; ......[1]

where

m is the slope of the line and

`(x_1, y_1)` are the coordinates of a given point on the line.

As per the given condition we have;

`(x_1, y_1)` = (-7, 5)

Slope(m) = 1/2

then; substitute these in [1] we have;

`y -5 = (1)/(2)(x-(-7))`

or

`y -5 = (1)/(2)(x+7)`

Using distributive property;
`a\cdot(b+c) = a\cdot b + a\cdot c`

`y-5= (1)/(2)x+(7)/(2)`

Add 5 on both sides we get;

`y=(1)/(2)x+(7)/(2) + 5`

Simplify:

`y= (1)/(2)x+(17)/(2)`

Only option which satisfy the above line equation is (9, 13).

Check:

put x = 9 and y = 13

`13= (1)/(2)(9)+(17)/(2)`

`13=(9)/(2)+(17)/(2) =(26)/(2) = 13` True.

Therefore, the another point that the line passes through is, (9, 13)

Answer 2

Selection C is appropriate.

_____
The change in x for the offered points is -6, -2, 16, 20, so the slope of 1/2 will make the change in y be -3, -1, 8, 10. When added to 5, these values are 2, 4, 13, 15. Only 13 matches the second coordinate of the given answer, so only (9, 13) will be a point on the line.