Algebra 1A- Unit 2- Post Test: Linear Equations

A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation y = mx + b. A line is drawn on the coordinate plane that passes through the point (10,1) and has a slope of -0.5. The y-intercept of the line is____________.

6

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?

-4

Which statement is true about this equation? -9(x + 3) + 12 = -3(2x + 5) − 3x

The equation has infinitely many solutions.

Which equation is equivalent to the formula below? y = a(x - h)^2 + k

a = y - k/ (x - h)^2

Order each step and justification that is needed to solve the equation below. 2/3y + 15 = 9

★2/3y + 15 - 15 = 9 - 15 Subtraction property of equality ★2/3y = -6 Simplification ★2/3y ● 3/2 = -6 ● 3/2 Multiplication property of equality ★y = -9 Simplification

Find the mistake made in the steps to solve the equation below. 6x - 1 = -2x + 9 ★8x - 1 = 9 Addition property of equality ★8x = 10 Addition property of equality ★x = 8/10 Division property of equality ★x = 4/5 Simplification

Step 3 is incorrect and should be x = 10/8

A rectangular section of granite is being cut so that the length is 3 times the width. The perimeter of the section must be less than 320 inches. Which statement is true?

The length of the granite must be less than 120 inches.

Currently, Nora is 3 times as old as Damon. In 8 years, she will only be 2 times as old as Damon. How old will Damon be in 8 years?

16 years old

Michael solved this inequality as shown: Step 1: -6(x + 3) + 10 < -2 Step 2: -6x − 18 + 10 < -2 Step 3: -6x − 8 < -2 Step 4: -6x < 6 Step 5: x > -1 What property justifies the work shown between step 3 and step 4?

addition property of inequality

Which value of n makes this equation true? 3n + 3/5 = 5n - 1 /9

n = -16

Jamal is comparing his transportation options for an upcoming trip. He's considering a rental car and a taxi service. Based on his planned routes during his trip, he expects a taxi service would cost about $128. Jamal could also get a rental car for a daily rate and unlimited miles. If Jamal's trip will last 4 days and he expects to pay about $24 for gas, which graph shows the range of car rental rates that would be cheaper than the taxi service?

open point on 26 going left x < 26

Paula used these steps to solve an equation: Step 1: -4(x + 8) - 2x = 25 Step 2: -4x - 32 -2x = 25 Step 3: -6x - 32 = 25 Step 4: -6x = 57 Step 5: x = -9 1/2 Between which two steps did Paula use the division property of equality?

steps 4 and 5

Given the following formula, solve for t. v = u + at

t = v - u/ a

What is the justification for step 2 in the solution process? 10x − 25 − 3x= 4x − 1 Step 1: 7x − 25= 4x − 1 Step 2: 7x= 4x + 24

the addition property of equality

Which graph represents the solution to this inequality? -1/4(12x + 8) ≤ -2x + 11

the closed ray on -13 going right x ≥ -13

An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals. If none of the animals get adopted, which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?

x < 27

What is the solution for x in the equation? 16x − 4 + 5x = -67

x = -3

What is the solution for x in the equation? -x + 3/7 = 2x - 25/7

x = 4/3

Which equation is correctly rewritten to solve for y? 12y + d = -19y + t

y = t - d/ 31