Answer:
m = 1, b = -3 ➜ x - y = 3
m = 1, (-1, 2) ➜ x - y = -3
(-2, 3), (-3, 4) ➜ x + y = 1
Step-by-step explanation:
This is asking us to match up information and equations. The information given is either a slope (m = ) and y-intercept (b = ), a slope and a coordinate point, or two coordinate points.
First, we will rewrite the given equations in slope-intercept form to help us match up the ones with a slope. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
x + y = 1 ➜ y = -x + 1
x - y = 1 ➜ y = x - 1
x - y = -3 ➜ y = x + 3
x - y = 3 ➜ y = x - 3
We can now match the first one (m = 1, b = -3) with x - y = 3.
The second one must be x - y = -3 because it is the only answer option where m = 1 and substituting x = -1 gives y = 2.
x - y = -3 ➜ (-1) - (2) = 1 ➜ - 1 -2 = -3 ✓
Finally, we will substitute in (-2, 3) into the two remaining options. Since this only works for one of them, we know that this is our answer and do not need to check (-3, 4).
x + y = 1 ➜ -2 + 3 = 1 ➜ 1 = 1 ✓
x - y = -3 ➜ -2 - 3 = -3 ➜ -5 = -3 ✗
I have also graphed the given equations and coordinate points, see the attached image. I have color-coded the given equations with the correct information given.
