Understanding Linear Equations and Relationships
Explore various questions related to linear equations, slopes, y-intercepts, proportional relationships, and unit rates with step-by-step solutions and explanations. Practice identifying linear functions and graphing equations through real-life scenarios. Enhance your understanding of slope-intercept form and how to determine equations from given points and slopes.
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Question #1 An apartment costs $250 up-front and $900 monthly. Write the equation. ANS: y = 900x + 250
Question #2 There were 90 peppermints in Ms. Huynh s jar. Her students were taking them at a rate of 3 per minute. What equation describes what is happening to Ms. Huynh s peppermints? ANS: y = -3x + 90
Question #3 What is the slope and the y-intercept of the graph? ANS: m = 3 or 3/1 b = (0, 3)
Question #4 What is the slope of the line with the following ordered pairs? X -1 0 1 2 Y 1 3 5 7 ANS: y = 2x + 3
Question #5 Does this table represent a linear function? Why? X -1 0 1 2 Y 1 3 5 7 ANS: Yes, it is a linear function. It has a constant rate of change.
Question #6 What is the equation of the graph? ANS: y = 3x + 3
Question #7 Does this table represent a proportional relationship? How do you know? X 0 1 2 3 Y 0 3 6 9 ANS: Yes, it is a proportional relationship. It has a constant comparison between the x and y (1:3) and the line goes through the origin.
Question #8 What is the unit rate of the line created by the ordered pairs in the table? X 0 1 2 3 Y 0 3 6 9 ANS: Unit Rate = 3 1
Question #9 A line passes through the point ( 5, 4) with slope m= 3. Write its equation in slope-intercept form. ANS: y = -3x 11 ***Steps: Use the slope-intercept form equation (y = mx+b) along with the given slope and coordinates to solve for b . 4 = -3(-5) + b 4 = 15 + b -15 = -15 -11 = 0 + b -11 = b Y = -3x - 11
Question #10 Graph the equation: Y = 1 ***Use the marker boards*** 4x 2 ANS:
Question #11 What is the equation of a line that passes through the points (-2, 5) and (1, -1)? ANS: y = -2x + 1 ***Steps: Common Difference: 1 5 1 ( 2) = 6 1) m = 3 = -2 2) To find the y-intercept, use one of the ordered pairs in the problem (1,-1) with the slope (-2) and solve for b from the slope-intercept form equation (y = mx + b): -1 = -2(1) + b -1 = -2 + b +2 =+2 1 = 0 + b 1 = b Y = -2x + 1
Question #12 What does the point (2, 27) mean in the graph? ANS: It means that in 2 weeks, Jack s gecko has eaten 27 crickets.
Question #13 Convert the following equation from Standard form to Slope-Intercept form: 4x y = 8 ANS: y = 4x 8 ***Steps: 4x y = 8 0 (1) y = -4x + 8 -4x = -4x -1 y = 4x - 8 -1
Question #14 Which function has the greater slope? ANS: Function A has the greater slope. Function A: m = 5 (Rise over Run!) Function B: m = 4
Things to Review for the TEST: Know the parts of the slope-intercept form of the equation and their meanings: Y = total M = slope (rate of change, ? ?) X = # of something (days, hours, sec, min, etc) B = y-intercept (starting point or initial amount/cost) How to find slope (3 methods) Common Difference Tables Graphing or Rise/Run Converting equations from standard form to slope-intercept form Unit rate Where x from the slope is equal to 1 Proportional relationship The constant comparison between x and y and its start at the origin (0,0) Continued on next slide .
Things to Review for the TEST: You should be able to: Compare tables, graphs, and equations Find the y-intercept from a table, graph, or equation Be able to write an equation from a word problem, graph, or table Be able to draw the graph of a line from a table or equation (and properly label the x- and y- axis If you have questions, message me on remind or email me at: huynhng@boe.richmond.k12.ga.us Study hard and prepare well!!- Ms. Huynh
