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?

Answer 1

Selection C is appropriate.

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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.

Answer 2

Answer:

Option C is correct.

Another point is, (9, 13)

Step-by-step 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;

$y -5 = \frac{1}{2}(x-(-7))$

or

$y -5 = \frac{1}{2}(x+7)$

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

$y-5= \frac{1}{2}x+\frac{7}{2}$

Add 5 on both sides we get;

$y=\frac{1}{2}x+\frac{7}{2} + 5$

Simplify:

$y= \frac{1}{2}x+\frac{17}{2}$

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

Check:

put x = 9 and y = 13

$13= \frac{1}{2}(9)+\frac{17}{2}$

$13=\frac{9}{2}+\frac{17}{2} =\frac{26}{2} = 13$           True.

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