Question

Which equation does the graph of the systems of equations solve?
−one half x + 3 = 3x − 4

−one half x − 3 = −3x + 4

one half x + 3 = 3x + 4

one half x + 3 = −3x − 4

Answer 1

g

Answer 2

@mathmale @campbell_st

Answer 3

@kirbykirby

Answer 4

Well there are a few ways to approach this... especially since it's multiple choice.
1) You can plug in the solution (2,2) into both equations and see if the questions are satisfied
2) You can check which line has, ignoring the sign for now, the steepest slope (slope > 1) and the least steepest slope (slope between [0,1] ) and the determine their appropriate signs by the direction of the line:
/ is positive
\ is negative
And identify visually the y-intercept for the line you can see
3) Determine the actual equations of each line by picking two points on a line, then finding their slope. (The equation of the line being y= mx+ b, and m is the slope and b is the y-intercept). Once you find the slope, you can plug in into the equation of the line, a point on the line by replacing the y and x values in the equation with the values of the point, and then solve for b

Answer 5

ok so is the answer B

Answer 6

not quite

Answer 7

ok hold on

Answer 8

C?

Answer 9

@kirbykirby

Answer 10

The line like this:
\ is negatively sloped. An easy way to tell if the slope is between [0, 1] is to see that, if you look at two easily identifiable points (i.e where the coordinates are whole numbers), then you will see that there are more squares spanning in the horizontal (x-axis) direction, then in the vertical (y-axis direction).

Answer 11

This this allows you to see if this line is the one with slope of 1/2, or the slope of 3. And the sign is easy since the line is going this way \ , it is negative.

And then you can see the intercept graphically (it the number where the line crosses the y-axis)

Answer 12

All of those clues should lead you to one answer , without even having to worry about the 2nd line.

Answer 13

D?

Answer 14

the line has the form
y = mx + b

where m is the slope. Above, I hint that the slope of the first line should be -1/2, so so far you should get
\(y = \large \frac{-1}{2}x+b\)

Answer 15

ok its A

Answer 16

yes

Answer 17

how did i not see that

Answer 18

:)

Answer 19

thanks

Answer 20

can you help me on one more

Answer 21

sure