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The another point that passes through the line which already passes through (-7, 5) and has a slope of 1/2 is (9, 13). The correct option is C.
What is the equation of a line?
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given the slope of the line as 1/2 and the coordinate of the point as (-7,5) through which the line passes. Therefore, the y-intercept of the line can be found by substituting the slope and the coordinate of the point in the equation of the line.
y = mx + c
5 = (1/2)(-7) + c
5 = -3.5 + c
5 + 3.5 = c
c = 8.5
Now, the equation of the line is y=(1/2)x+8.5.
Further, substitute the points in the equation to check if the point li on the line.
1.) (-13,9)
y = (1/2)(-13) + 8.5
y = -6.5 + 8.5
y = 2
Not the point.
2.) (-9,13)
y = (1/2)(-9) + 8.5
y = -4.5 + 8.5
y = 4
Not the point.
3.) (9,13)
y = (1/2)(9) + 8.5
y = 4.5 + 8.5
y = 13
The point lies on the line.
4.) (13,9)
y = (1/2)(13) + 8.5
y = 6.5 + 8.5
y = 15
Not the point.
Hence, the correct option is C.
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