3 The graph shows a line that goes through the points (-6, -3) and (4, 2). Which TWO statements are true...

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Question 1-3
The graph shows a line that goes through the points (-6, -3) and (4, 2).
Which TWO statements are true about the line?
□ The line goes through the point (0, 5).
□ The line has a positive slope.
□ The line shows a direct variation.

SnapAndSolve AI · Accepted Answer

To determine if the line goes through the point (0, 5), we need to find the equation of the line. The slope (m) is calculated as follows:

m = (y2 - y1) / (x2 - x1) = (2 - (-3)) / (4 - (-6)) = 5 / 10 = 0.5

The equation of the line in point-slope form is:

y - y1 = m(x - x1)

Using point (-6, -3):

y + 3 = 0.5(x + 6)

Convert to slope-intercept form (y = mx + b):

y = 0.5x + 0

Thus, the y-intercept is 0, not 5. Therefore, the line does not go through the point (0, 5).
The line has a positive slope of 0.5.
The line shows a direct variation because it passes through the origin (0, 0) and can be expressed in the form y = kx, where k is a constant (0.5 in this case).

Correct statements:

The line has a positive slope.
The line shows a direct variation.

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3 The graph shows a line that goes through the points (-6, -3) and (4, 2). Which TWO statements are true...

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