Question

In a video game, Bob can score 3 points (x) or 4 points (y) by hitting targets. To win the game he must score at least 20 points. Which graph shows all the ways Bob can win the game

Answer 1

3x + 4y >= 20
disregard the > sign at the moment.
We need to find the x and y intercepts of this graph. To find the x intercept, we sub in 0 for y.
3x + 4(0) = 20
3x = 20
x = 20/3 (for the graph, it is (6 2/3,0) --- that is 6 and 2/3
To find the y intercept we will go ahead and put the inequality in y = mx + b form.
3x + 4y >= 20
4y >= -3x + 20
y >= (-3/4)x + 5
In y = mx + b form, the m stands for the slope and the b stands for the y intercept. So our slope is -3/4 and our y intercept is 5....for graphing purposes that is (0,5)

So map your points (6 2/3,0) and (0,5).....connect the points with a solid line because of the equal sign in the problem. Also, the your points will be marked with a solid circle. And since y >= -3x + 5....the shading will occur above the line. If you want to use your slope (-3/4), start at the y int (0,5) and and come down 3 spaces, then go right 4 spaces...keep doing this and your should land on the x int.
It should look something like this...and all that scribble is where the shading is.