On Desk: Learning Log: HW: p. 49, #20, 21, #22-25 (a only!), #43 Math CC7/8 – Be Prepared On Desk: Pencil Calculator Math Journal TwMM Learning Log Plickers Card from Mrs. Miner 2 half sheets from counter Learning Log: HW: p. 49, #20, 21, #22-25 (a only!), #43

Tasks for Today Finish Lesson 2.3? Warm Up – Writing equations Lesson 2.4 – Inequalities, Solving Linear Equations

Dana’s work is correct. In general, if you know the slope of a line and a point on the line you can substitute these three values in for y, m, and x in the equation y = mx + b and solve the equation for b.

y = 2x – 3. The equation should be No, Chris has not used the coordinates of the two points correctly to find the slope. She put the differences in x on top! It should be the change in y divided by the change in x, for a slope of 2.

Warm Up Find an equation for the line that satisfies the conditions.

greater than or equal to What are inequalities? Symbol Words Example Use = equals 1 + 1 = 2 ≠ not equal to 1 + 1 ≠ 1 > greater than 5 > 2 < less than 7 < 9 ≥ greater than or equal to marbles ≥ 1 ≤ less than or equal to dogs ≤ 3

What is an inequality? An inequality is similar to an equation. There are two expressions separated by a symbol that indicates how one expression is related to the other. In an equation such as 7x = 49, the = sign indicates that the expressions are equivalent. In an inequality, such as 7x > 49, the > sign indicates that the left side is larger than the right side. To solve the inequality 7x > 49, we follow the same rules that we did for equations. In this case, divide both sides by 7 so that x > 7. This means that x is a value and it is always larger than 7, and never equal to or less than 7.

$ 0.15 = the cost per minute of rental time $2.50 = the fixed charge for renting

Solve for t… $9.25 = 0.15t + 2.50 -2.50 - 2.50 6.75 = 0.15t 0.15 0.15 45 = t 2. Use substitution! c = 0.15t + 2.50 c = 0.15(25) + 2.50 c = $6.25

Hint: Use an inequality! -2.50 - 2.50 3.50 ≥ 0.15t 0.15 0.15 23.3 ≥ t She can use the canoe for no more than 23 and 1/3 minutes, or about 23 minutes or less.

You can easily estimate the y-intercept. (2.50) You can use it to calculate the slope. (0.15) You can find 25 min on the x-axis and estimate the cost from the y-axis. You can find $9.25 on the y-axis and estimate the time for that charge. You can use it to find all the times that would lead to a cost of no more than $6.

You can calculate the slope by finding the change in y (rental charge) as x (time) increases by 1 minute. (slope = 0.15) You could work backwards and find the y value for when x is 0. (y-intercept = 2.50) You can find the y-value (cost) for 25 min. by finding the point between 20 and 30 on the table. You can find the time for $9.25 by finding the point between 40 and 50 minutes. You can find the rental time for no more than $6 by looking at the rental charge row and seeing it would be just over 20 minutes.

Yes, they are correct! They subtracted 2.50 from each side of the equation and then divided by 0.15 on each side of the equation.

She can use the canoe for no more than 23 and 1/3 min She can use the canoe for no more than 23 and 1/3 min., or about 23 min. or less.

Solve for t… $9 = 4 + 0.10t -4 - 4 5 = 0.10t 0.10 0.10 50 = t Use substitution! c = 4 + 0.10t c = 4 + 0.10 (20) c = $6

$12 ≥ 4 + 0.10t -4 - 4 8 ≥ 0.10t 0.10 0.10 80 ≥ t Hint: Use an inequality! You can use the paddle boat for no more than 80 minutes, or an hour and 20 minutes or less.