Name Algebra 1B review problem set
June 17, 2009 Review #4: Lines and linear systems page 5
Review #4: Lines and linear systems
Summary
· Slope of a line: m == .
□ Parallel lines have equal slopes; perpendicular lines have opposite reciprocal slopes.
· Equation forms for lines
□ slope-intercept form: y = mx + b where m is the slope, b is the y-intercept.
□ point-slope form: y = m(x – x1) + y1 where m is the slope, (x1, y1) is a point on the line.
□ horizontal line: y = a number
□ vertical line: x = a number
· Methods for graphing lines
□ for any y = form: first make an input-output table, then make the graph from the table
□ for slope-intercept form: draw the y-intercept then use slope to locate other points
□ for point-slope form: draw (x1, y1) then use the slope to locate other points
□ for Ax + By = C form: put in 0 for x, find y; put in 0 for y, find x; this gives the 2 intercepts
· Ways to solve a system of two linear equations
□ substitution (solve one equation for one variable; substitute in the other equation)
□ elimination (add multiples of the equations to make a variable drop out)
□ graphing the lines and finding their intersection (on paper, or 2nd Trace Intersect on calculator)
Problems
1. Write a linear equation for each of the following.
a. the line through the points (1, –7) and (–3, 3)
b. this tablex / y
2 / 14
4 / 10
6 / 6
8 / 2
10 / –2
/ c. this graph / d. this graph
e. the vertical line through the point (3, 4)
2. Graph these equations without using your calculator. Try to choose the easiest method based on what type of equation you’re given.
a. y = / b. y = 2(x – 1) – 4 / c. 4x – 3y = 123. a. Write an equation for the line given in the graph.
b. Write equations for two lines that are parallel to the given line.
c. Write equations for two lines that are perpendicular to the given line.
d. Write an equation for a line that is parallel to the given line and goes through the point(2, 3). Use point-slope form.
4. Here is a system of two linear equations: y = 2x – 3, 3x + 6y = 12
a. Answer this question without solving the system: Is (4, 5) a solution to the system?
Answer (circle): yes no
Show work here:
b. Solve the linear system by graphing two lines on the grid, and finding their intersection.
c. Solve the linear system again, using the substitution method. Make sure you get the same answer.
5. Here is a system of two linear equations: –5x + y = 21, 3x – 2y = –14.
a. Solve the system using the elimination method.
b. Go back to the original equations: –5x + y = 21, 3x – 2y = –14.
Perform the algebra steps to solve each of these equations for y.
c. Now solve the system again using graphing on your calculator.
Show your work on the screens below. You should get the same answer as in part a.
Intersection: ______
6. Solve these linear systems using elimination. (Unusual things happen in these problems.)
Name Algebra 1B review problem set
June 17, 2009 Review #4: Lines and linear systems page 5
a. 2x – 4y = 10
3x – 6y = 15
b. –4x + 3y = 5
–8x + 6y = 12
Name Algebra 1B review problem set
June 17, 2009 Review #4: Lines and linear systems page 7
7. Jose and his relatives go to a water park together. Admission costs $24.95 for adults and $17.95 for children. In all, 12 people go to the water park, and the total spent for the family’s tickets is $250.40. How many adults and how many children were there?
a. Set up a linear system that represents the problem. Tell what x and y stand for.
b. Solve the system of equations using the substitution method.
c. Check your solution by graphing on the calculator and finding the intersection.
Show your work on the screens below.
Intersection: ______
8. At Fenway Park, they sell Fenway Franks (hot dogs) and big sodas in souvenir cups.
Keith’s family buys 3 Fenway Franks and 2sodas, and pays $23.
Ayida’s family buys 8 Fenway Franks and 5 sodas, and pays $59.50.
What are the selling prices for Fenway Franks and for sodas?
a. Set up a linear system that represents the problem. Tell what x and y stand for.
b. Solve the system of equations using the elimination method.
c. Check your solution by substituting into the original equations, and showing that it makes both equations true.
Calculator review: linear regression
Here is a review of the steps for doing linear regression (finding a best-fit line) on your calculator.
Step 1: Enter the data under [STAT] Edit in columns L1 and L2.
Step 2: Make a scatter plot by pressing [2nd]STATPLOT, then 1:Plot1, then choosing “On” and the icon that looks like a scatter plot, then finally [GRAPH]. If you can’t see the graph, [ZOOM][9].
Step 3: Get the linear regression equation using [STAT]CALC 4:LinReg [ENTER][ENTER].
Step 4: Graph the line on top of the data by starting from an empty [Y=] screen then typing [VARS][5][à][à][ENTER][GRAPH].
number offarmers / number of pigs
1 / 15
8 / 230
10 / 380
4 / 135
2 / 65
1 / 30
4 / 93
3 / 82
2 / 49
12 / 411
You try it
9. The data table shows the number of farmers and the numberof pigs at each of ten different farms. This problemisabouthow these two numbers are related.
Let x = the numberof farmers, y = the number of pigs.
a. On your calculator, find the best-fit line equation:
y = ______x + ______
b. Graph both the data points and the best-fit line on your calculator screen. Draw your calculator screen:
c. Use your best-fit line equation to predict how many farmers there would be at a farm with 170 pigs.
d. Use your best-fit line equation to predict how many pigs there would be at a farm with 9farmers.