Graphing Systems
When graphing a slope-intercept form of a linear equation, what are the steps to graph it?
1. Plot the y-intercept.
2. Move according to the slope and plot a second point.
3. Connect the two points.
Use substitution to solve the system. Answers should be in the form of a coordinate point.
y = 5
y = 3x – 7
(4, 5)
Use elimination to solve the system. Answers should be in the form of a coordinate point.
4x + y = 8
–3x – y = 0
(8, –24)
Name a number that is an integer, but not whole.
ex. negative numbers
Is (1, 6) a solution to this system of linear equations?
y = -4x + 10
8x + 2y = 20
Yes because these are actually the same equation. If we solve for y for the second equation, we get 2y = -8x + 20 and then we can divide by 2 and we get y = -4x + 10. Since they are the same equation, they are coinciding lines so every point for one equation is also true for the other!
Convert this standard form equation into a slope-intercept form equation: 8x + 2y = –2.
y = –4x – 1
Is the point (5, 13) a solution to the system? Why or why not?
y = 4x – 7
y = 2x + 9
No, (8, 25) is the solution. (5, 13) works for the first equation, but not both!
Use elimination to solve the system. Answers should be in the form of a coordinate point.
x – y = 13
3x – y = 19
(3, –10)
Is 9 is an integer.
yes
What quadrant does the solution of the system fall into?
y = –4
x = 2
Quadrant 4
Find the x and y intercepts of 3x + 2y = –10
x-intercept: (–10/3, 0)
y-intercept: (0, –5)
Use substitution to solve the system. Answers should be in the form of a coordinate point.
8x + 2y = –2
y = –5x + 1
(2, –9)
Use elimination to solve the system. Answers should be in the form of a coordinate point.
2x + 5y = 20
3x – 10y = 37
(11, –2/5)
If a number is natural, then it also whole. (true/false)
true
Write an equation for a line that is perpendicular to this one:
y = -5x + 3
Complete the sentences....
The line x = –4 is a ___________ line.
The line y = 7 is a ___________ line.
1. vertical
2. horizontal
Use substitution to solve the system. Answers should be in the form of a coordinate point.
y + 2x = –1
y – 3x = –16
(3, –7)
Use elimination to solve the system. Answers should be in the form of a coordinate point.
3x + 2y = –5
2x – 5y = 3
(–1, –1)
Is Zero is an natural/counting number.
no
They need to have the same slope so that they won't ever intersect. Using the same slope, they will always be moving in the same direction at the same rate, so they won't touch. They cannot, however, have the same y-intercept because that would mean that they share a point and that is not possible for parallel lines. If they had the same slope and the same y-intercept, then they would be coinciding lines, not parallel lines.
Graph and describe the system:
x + 3y = 5
–2x – 6y = – 10
They are the same lines, so they are dependent and consistent.
Use substitution to solve the system. Answers should be in the form of a coordinate point.
3x + y = –4
–2x + 5y = –54
(2, –10)
Use elimination to solve the system. Answers should be in the form of a coordinate point.
y = –4x + 7
8x + 2y = 10
False statement-> no solution-> parallel lines
is .66666 a rational or irrational number? Why?
yes,
The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus and name the number category that the solutions must fit into!
The van holds 8 students and the bus holds 22 students; both are whole number solutions because we cannot have a decimal/negative number of students so integers, irrational, rational, imaginary, do not work. Also, we can have 0, so natural numbers also do not work.