Answer:
(b) x +2y = 8
Step-by-step explanation:
There are at least a couple of ways to come to the conclusion.
1) use the given information to write the equation of the desired line
2) check to see which of the answer choices satisfies the requirement
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1)
The given line has two specified points on it. These can be used to find its slope. (Or, you can count grid square to see it has a rise of -1 for a run of +2.)
The slope formula is ...
m = (y2 -y1)/(x2 -x1)
m = (-4 -0)/(4 -(-4)) = -4/8 = -1/2
Comparing this to our grid square count, we see they are the same:
m = rise/run = -1/2
Now, we have a slope (-1/2) and a point (2, 3), so we can use these to write the point-slope equation of the desired line:
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
y -3 = -1/2(x -2) . . . . . point-slope equation of the desired line
y -3 = -1/2x +1 . . . . . . eliminate parentheses
1/2x +y = 4 . . . . . . . . add 1/2x +3 to both sides
x +2y = 8 . . . . . . . . . multiply by 2
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2)
Perhaps easier in this case is to try the given equations to see which is satisfied at the given point. There are two different left-side expressions to evaluate at the point (x, y) = (2, 3):
x +2y = (2 +2(3)) = 2+6 = 8
2x +y = 2(2) +3 = 4 +3 = 7
Only the equation ...
x +2y = 8
is satisfied at the given point.
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Additional comments
While I encourage you to learn to solve questions like this "from scratch", modern math curriculum is often "multiple choice."
When faced with multiple choices for answers, it is often easiest to ...
(a) eliminate the ones that are not self-consistent or that are false on their face;
(b) eliminate the ones that have an obviously fatal flaw (wrong sign of slope, too large or too small, for example);
(c) choose from the remaining ones the one that properly answers the question (satisfies all requirements).
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When you solve a standard-form equation for y, you get ...
ax +by = c
by = -ax +c
y = -a/bx +c/b
That is, the slope of the line is -a/b.
For the two left-side expressions in the answer choices, the slopes are ...
x +2y ⇒ slope = -1/2
2x +y ⇒ slope = -2/1 = -2
The scales on the graph are the same in the x- and y-directions, so the shallow negative slope of the given line is clearly less than 1. That eliminates the last two answer choices already.
