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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)

Respuesta :

sqdancefan
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.
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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 [tex]y-y_1=m(x-x_1)[/tex];               ......[1]

where

m is the slope of the line and

[tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.

As per the given condition we have;

[tex](x_1, y_1)[/tex] = (-7, 5)

Slope(m) = 1/2

then; substitute these in [1] we have;

[tex]y -5 = \frac{1}{2}(x-(-7))[/tex]

or

[tex]y -5 = \frac{1}{2}(x+7)[/tex]

Using distributive property; [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]

[tex]y-5= \frac{1}{2}x+\frac{7}{2}[/tex]

Add 5 on both sides we get;

[tex]y=\frac{1}{2}x+\frac{7}{2} + 5[/tex]

Simplify:

[tex]y= \frac{1}{2}x+\frac{17}{2}[/tex]

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

Check:

put x = 9 and y = 13

[tex]13= \frac{1}{2}(9)+\frac{17}{2}[/tex]

[tex]13=\frac{9}{2}+\frac{17}{2} =\frac{26}{2} = 13[/tex]           True.

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


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