Answer:
The correct answer is shown selected.
Step-by-step explanation:
I believe it is helpful here to find the slope of the line as a starting point. Then that can be used to compare to the offered equations, or to derive the equation for the line from scratch.
<em>Slope of the line</em>
The two points differ in y-value by 3 and in x-value by 5. The y-value gets smaller (more negative) as the x-value increases, so the slope is ...
... (change in y)/(change in x) = -3/5
<em>Derive the equation for the line</em>
In point-slope form, the equation of the line can be written as ...
... y - k = m(x - h) . . . . . for point (h, k) and slope m
Choosing the upper-left point (-3, 2) and using the slope we found, this equation becomes ...
... y - 2 = (-3/5)(x - (-3))
Multiplying by 5 (to eliminate the fraction), this is
... 5y -10 = -3x -9
Adding 10 + 3x to both sides gives ...
... 3x + 5y = 1 . . . . . . matches the last selection
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<em>Making use of what you know</em>
The slope of a line is the coefficient of x when you solve for y. Starting from ...
... ax +by = c
and solving for y, we can subtract the x-term, then divide by the y coefficient. This gives ...
... y = (-ax +c)/b = (-a/b)x +c/b
That is, <em>the slope of line ax+by=c is -a/b</em>.
In order, top to bottom, the slopes of the lines in the answer choices are ...
... -1/5, -1/3, -5/3, -3/5
Only the last choice matches the slope of the graphed line.
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<em>Checking the offered answers</em>
Another way to choose the correct answer is to see if the points on the graph satisfy the answer equation. Using the point (x, y) = (-3, 2), we can see ...
- -3 + 5(2) = 7 ≠ 3 . . . . first answer doesn't work
- -3 + 3(2) = 3 ≠ 5 . . . . second answer doesn't work
- 5(-3) +3(2) = -9 ≠ 1 . . third answer doesn't work
- 3(-3) +5(2) = 1 . . . . . . . this answer checks OK
If you were to find more than one equation that works with this point, you would check the other point.
