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.
Slope of the line
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
Derive the equation for the line
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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Making use of what you know
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, the slope of line ax+by=c is -a/b.
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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Checking the offered answers
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.
