Graphing Linear Equations
m=slope
b=y-intercept
Create the equation of a line that has slope 2 and contains the point (0,5)
y=2x+5
Solve the system of equations:
3x - 2y = 10
3x + 5y = 17
(7,1)
When you graph an inequality that is > or <, do you use dotted or solid lines?
Dotted
f(4) = 5
For the equation 4x-5y=3, what is the slope?
m=4/5
Create the equation of a line that has slope 1/2 and contains the point (-4,1)
y=1/2x+3
Solve the system of equations:
3x - 2y = 10
4x + y = 6
(2, -2)
When graphing inequalities, if it is > or ≥, will you shade below the line or above the line?
above the line
For f(x) = 2x - 3 and g(x) = x2 + 1, find f(g(4)).
f(17) = 2(17) - 3 = 34 - 3 = 31
f(g(4)) = 31
For the equation 2x = 3 - 4y, what is the y-intercept?
3/4
Create the equation of a line that is parallel to y=-3x+2 and contains the point (4,-5).
y=-3x+7
Solve the system of equations:
3x - y = 2x - 7
2x + 5 = 2y - 9
Inifinite Solutions
Graph the inequality:
2x - 3y ≥ 6
Change to y ≤ 2/3x - 2
Intercepts at (0,-2) and (3,0) with a solid line, shaded below.
A linear function contains the points (-2, 5), (0, 10), and (2, 15). What will y be when x is 6?
We are increasing by 2 in the x, and 5 in the y. So the next points are (4, 20), (6, 25). So y = 25.
Graph the equation 4x + 3y = 6.
Change to y = -4/3x + 2 with intercepts at (0,2) and (3/2,0).
Create the equation of a line that is perpendicular to y=-3x+2 and contains the point (6,-2).
y=1/3x-4
2x = 11 - 6y
3y = 6 - x
No Solution
Solve the system of inequalities by graphing:
4x - 3y ≥ 10
2x ≤ y + 6
Change to y ≤ 4/3x - 3 1/3 and
y ≥ 2x - 6
Intersect at (4,2) and shaded between them on bottom left.
Find an equation for the linear function where f(3) = 7 and f(-1) = 5.
Graph the equations x=3 and y=-2.
x=3 is vertical at 3 on the x-axis.
y=-2 is horizontal at -2 on the y-axis.
Create the equation of a line that passes through the point (3, 5) and (-1, 2).
y=3/4x+11/4
A theater production charges $21 for adult tickets and $15 for student tickets. If the production sold 102 tickets for its opening night and made $1,932 in ticket sales, how many of each type of tickets were sold?
67 adult tickets and 35 student tickets were sold.
Solve the system of inequalities by graphing:
2x - 3y < 5
4x > 3 + 6y
Change to y > 2/3x - 5/3 and
y < 2/3x - 1/2
Parallel and shaded between them.
A plumber costs $110 for 3 hours and $160 for 5 hours. How much would 8 hours cost?
The points are (3, 110) and (5, 160). The slope is 50/2 = 25.
110=25*3 + b
110-75 = 35 = b so y = 25x + 35 is the equation and y= 25*8 + 35 = $235