hint: ignore the green and yellow for now, just focus on the two black lines write the equations for the lines in point intercept form
uh... not quite
|dw:1443914795869:dw| lets focus on one line at a time. what is the equation of this line?
|dw:1443914881362:dw| write the equation for this line please
nope first find the slope of the graph
(x1,y1) = (-3,0) (x2,y2) = (0,3) slope = m = (y2-y1)/(x2-x1) = ?
keep going (0-3)/(-3-0) = ?
-3 and -3
/ means divide...
-3/-3 = ?
good, so our slope is 1 now find the y-intercept
good, so our equation is y = x + 3 now write an equation for the other line
0,3 and -1, 2?
uh not quite
look at the graph and pick two points on the line on the right
ill i can see is 3/ 1.5
two points are (0,3) and (2,-1) now calculate the slope between them
slope = (y2 - y1) / (x2 - x1) (0,3)....x1 = 0 and y1 = 3 (2,-1)....x2 = 2 and y2 = -1 now we sub slope(m) = (-1 - 3) / (2 - 0) slope(m) = -4/2 slope(m) = -2 now we use y = mx + b slope(m) = -2 use either of your sets of points....(0,3)...x = 0 and y = 3 now we sub into the formula to solve for b, the y intercept 3 = -2(0) + b 3 = b so the equation for that line is : y = -2x + 3
now take your 2 lines... y = x + 3 and y = -2x + 3 notice that both lines are solid...this means they both contain equal signs. notice that both lines are shaded below the line....this means that both lines are less then <. so the inequalities that match the graph are : y <= x + 3 and y <= 2x + 3
This is how you solve this quickly since we are given choices. 1. Both lines are solid; that means either >= or <=, but not > or <. 2. Both lines have the shaded area under the solid line. That means y <= ax + b. 3. Both lines have y-intercepts of 3. That means both inequalities are of the form y <= ax + 3 The only set of inequalities that satisfies all conditions above is choice A. Of course, this is assuming that where you wrote "less than or greater to" you really meant "less than or equal to."