Question

The coordinate grid shows the graph of four equations:

A coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. Line A passes through the ordered pairs negative 3, 4 and 9, negative 2. Line B passes through the ordered pairs 2, 8 and 8, negative 8. Line C passes through the ordered pairs negative 3, negative 4 and 4, 6. Line D passes through the points 2, negative 2 and 5 and 6.
Which set of equations has (3, 1) as its solution? (5 points)


A and B

C and D

B and D

A and D

Answer 1

The equation of Line A can be found using the slope-intercept form formula: y = mx + b, where m is the slope and b is the y-intercept.

m = (4 - (-2))/(-3 - 9) = 6/-12 = -1/2

Using point-slope form with the point (-3, 4) we have y - 4 = -1/2(x + 3). This simplifies to y = -1/2x + 1.5

So, Line A is y = -1/2x + 1.5

The equation of Line B can be found using the same method:

m = (8 - (-8))/(2 - 8) = 16/-6 = -8/3

Using point-slope form with the point (2, 8) we have y - 8 = -8/3(x - 2). This simplifies to y = -8/3x + 32/3

So, Line B is y = -8/3x + 32/3

Now, we can test if the point (3, 1) is a solution for each equation:

For Line A: 1 = -1/2(3) + 1.5, 1 = -1.5 + 1.5, 1 = 1

For Line B: 1 = -8/3(3) + 32/3, 1 = -8 + 32/3, 1 = 16/3

Therefore, the set of equations that has (3, 1) as its solution is A and B.