Presentation on theme: "Finding the Equation of a Line"— Presentation transcript:
1Finding the Equation of a Line To find the equation of a line you need to know the slope and y-intercept!
2Instructions There are 12 practice problems in this packet. Record the answers to each problem on a sheet of notebook paper, along with any work that may be necessary to arrive at the answers.Check each answer before advancing to the next problem. If you get one wrong, rework it until you can get the right answer; this is a study tool after all.Turn in your paper for an easy 100!You will not be penalized if you do not turn in your paper; this review is to help you, not hurt you! However, if you do not take it seriously, you will only hurt yourself!
3Slope-Intercept Form The slope-intercept form of a linear equation is… y = mx + bWhere “m” is the slope and “b” is the y-intercept.
4Writing the equation of a line when given the slope and y-intercept: Write the equation of a line with a slope of ½ and a y- intercept of -6:Answer: y = ½ x – 6Write the equation of a line with the following characteristics: b = 2; m = -5Answer: y = -5x + 2
5Finding the Equation when given the Slope & a Point on the Line In the equation y = mx + b, replace y, m, & x with the values given.Solve for b.Now that you know the slope and y-intercept, write the equation.Example: Find the equation of a line that passes through the point (8, -4) and has a slope of = (-2)8 + b -4 = b (Add 16 to both sides) 12 = b y = -2x + 12
6Practice Problem #1Which function represents the line that contains the point (2, 12) and has a slope of -3?A. f(x) = -3x + 6B. f(x) = -3x + 18C. f(x) = -3x + 34D. f(x) = -3x + 38Check Answer
7Practice Problem #2Which graph best represents the line that has a slope of and contains the point (4, -3)?A. C.B. D.Check Answer
8FINDING THE SLOPEIf you are given two points, the first step in any of the methods is to find the slope from the two given points, using the slope formula.
9Or Use [STAT] Edit First, find the slope: Example 1: A line passes through the two points (-4, 1) and (2, 5). Find the equation of this line.First, find the slope:Next, use the slope & one of the points to solve for the y-intercept, b.Now that you know the slope & y-intercept, write the equation:Or Use[STAT] Edit
10Using the Graphing Calculator… [STAT] EditEnter the x-values of the two points in List 1Enter the y-values of the two points in List 2
11To find the equation of the line… [STAT] CALC4: LinReg[ENTER]Write the equation on your paper.Convert the decimal numbers to fractions use the [MATH] button; see next slide .
12Converting Decimals to Fractions… Enter (all the way across the screen)[MATH] [ENTER] [ENTER]EnterWrite the Equation:
13Practice Problem #3What is the y-intercept of the function shown in the graph?A. -24B. -21C. -18D. -9(Hint: Find the equation of the line using the two points given; graph it on your calculator; view the table to find the value of y when x = 0.(10, 17)(6, 3)Check Answer
14Practice Problem #4Which of the following describes the line containing the points (0, 4) and (3, -2)?y = -2x + 4y = ½ x + 6y = 2x + 4y = - ½ x + 6Check Answer
15Standard Form of a Linear Equation The standard form of a linear equation is… Ax + By = C Where A is the coefficient of x, B is the coefficient of y, and C is the constant.
16Converting from Slope-Intercept Form to Standard Form To convert from y = mx + b to Ax + By = C, move the term that includes x to the left side of the equation.When writing linear equations in standard form, there are two things you must remember:1) The leading coefficient – which is the coefficient of x – must be positive; and2) No fractions are allowed! To get rid of the fractions, multiply the entire equation by the least common denominator (LCD).
17Examplesy = - ½ x + 6 ½ x + y = 6 (Add ½ x to both sides.) 2( ½ x + y = 6) Multiply everything x 2) x + 2y = 12Y = ⅓x – ½-⅓x + y = - ½ (Subtract ⅓x from both sides)-6(-⅓x + y = - ½ ) (Multiply everything x -6, the LCM of 3 & 2; you multiply by -6 instead of 6 in order to cancel the leading negative.)2x – 6y = 3Converting from slope-intercept form to standard form is sometimes necessary because, on TAKS, they often write the answer choices in standard form.
18Practice Problem #5Which equation best represents the line shown in the graph? A) 7x + 4y = 35 B) 4x – 7y = 35 C) 4x + 7y = -35 D) 7x – 4y = -35(7, -1)(0, -5)Check Answer
19Additional Practice Problems #6) Convert this equation to standard form:y = ⅜x – 4#7) Convert this equation to standard form:y = -⅔x + ⅜Check Answer Check Answer
20Converting from Standard Form to Slope-Intercept Form This is a very important skill because you cannot graph linear functions on your calculator unless the equation is written in slope-intercept form.When converting from standard form to slope- intercept form, your objective is to get y by itself.Example: 3x – 5y = 15-5y = -3x + 15 (Subtract 3x from both sides)Y = x – 3 (Divide everything by -5)
21Practice Problem #8At what point does the line 3x + 5y = 7 intersect the x-axis?Hint: Since the x-intercept is the point where the value of y = 0, replace y with 0 and solve for x.Check Answer
22Writing Equations from Tables of Data… XY-5-32571012When you are asked to find the equation that matches a table of data, enter the data into your calculator using [STAT] EDIT and perform a linear regression.Example, find the equation that matches this table of data.Click here for the answer.
23To match a Table to a Given Equation… Enter the equation in the Y= screen of your calculator.View the resulting table and compare it to the answer choices.
24Practice Problem #9Which table best represents the function y = 2x − 6? A. B. C.XY-3-121437-8XY-1431214720XY-3-122-2378Check Answer
25Practice Problem #10 Matt is a speed skater. His coach recorded the following data duringa timed practice period.If Matt continues to skate at the rate shown in the table, what is the approximate distance in meters he will skate in 20 seconds?A m B. 175 m C. 150 m D. 278 mTime(seconds)Distance(meters)4.50509.0010011.25125Check Answer
26Practice Problem #11 Check Answer A math club decided to buy T-shirts for its members. A clothing company quoted the following prices for the T-shirts.Which equation best describes the relationship between the total cost c, and the number of T- shirts, s?c = 6.75sc = 7.00sc = 2s – 20c = sNumber ofT-ShirtsTotal Cost(dollars)10751510520135Check Answer
27Practice Problem #12 End Show Which of the following tables contains values for an equation that has a slope of 4? A. B. C. D.End ShowCheck Answer
29Answer to Problem #1 Back B. y = -3x + 18 In the equation y = mx + b, replace y, m, & x with the values given & solve for b, as shown. Write the equation in slope- intercept form. Back
30Answer to Problem #2: Back D. In the equation y = mx + b, replace y, m, & x with the values given & solve for b, as shown. Write the equation in slope- intercept form; enter it in Y= and hit [GRAPH]. Back
31Answer to Problem #3: Back Enter the two points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.Perform a linear regression by using [STAT] CALC 4The value given for b is the y-intercept. Back
32Answer to Problem #4: Back A. y = -2x + 4Enter the two points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.Perform a linear regression by using [STAT] CALC 4 to find the equation. Back
33Answer to Problem #5 Back B. 4x – 7y = 35Convert the equation to standard form in order to find the correct answer:The y-intercept is -5.The slope is , which you can find by beginning at the y-intercept & counting up 4 & right 7 until you are at another identifiable point on the line.Once you know the slope & y-intercept, you can write the equation: Back
37Answer to Problem #9C. Enter the equation into the Y= screen of the calculator, view the resulting table and compare it to the answer choices. Be careful! Every ordered pair must match up; compare ALL of them, not just one or two. Back
38Answer to Problem #10: Back A. 222 mEnter the points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.Perform a linear regression by using [STAT] CALC 4 to find the equation.Enter the equation into Y=.View the table; find the y- coordinate when x = 20. Back
39Answer to Problem #11: Back D. c = sEnter the points in the [STAT] EDIT screen, with the x-values going in L1 and the y-values in L2.Perform a linear regression by using [STAT] CALC 4 to find the equation. Back
40Answer to Problem #12 B. Back Enter each table – one at a time – in the [STAT] EDIT screen & perform a linear regression.Look for the table which has a slope of 4, which is table B, as indicated below.This is the slope. Back