1. 4x + y > 4
2. 3x - 4y < 12
3. You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer.
4x + y >= 41. 4x + y > 4
y >= -4x + 4
this is a straight line with slope -4 and y-intercept 4. we want all values above this line. see graph1 below
3x - 4y < 122. 3x - 4y < 12
-4y < -3x + 12
y > (3/4)x - 3 .........since i divided both sides by a negative number, i turn around the inequality sign
now this is a line with slope 3/4 and y-intercept -3. we want all values above that line. see graph2 below
at least means you have greater than or equal to. a dime is 10cents, or $0.10, a quarter is 25 cents or $0.253. You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer.
let x be the number of dimes in the drawer
let y be the number of quarters in the drawer, then
0.10x + 0.25y >= 30
Hello, Patience,
to 1.:
4x + y ≥ 4 ==> y ≥ -4x + 4
y = -4x + 4 is a straight line. With your inequality you are looking for those points of the coordinate plane which are above this line. The graph of the inequality is a half plane where the border (= the straight line) is included to the half plane. (yellow + orange)
to 2.:
3x - 4y < 12 ==> y > 3/4*x - 3
You get a half plane too which is above the straight line but the border doesn't belong to the half plane! Therefore the straight line is dotted. (orange + brown)
EB