Linear Equations
Solve 3x + 7 = 22
x = 5
Identify the slope and y-intercept of y=4x-5
slope = 4. y-intercept = 5
solve: x+y = 10, x-y=2
(6, 4)
Two angles are complementary. One measures 37 degrees. Find the other angle
53
write equations for two linear graphs that are parallel
answers will vary but must have the same slope
Solve 5(2x-1) = 3x + 16
x = 3
Write the equation of the line with slope 3 and y-intercept -2
y = 3x - 2
Solve by substitution:
y = 2x + 1
x+y=10
(3,7)
Two corresponding angles are labeled (4x+10) and (6x−20). Find x
x = 15
Write the equation in point slope form for the point
(2, -1) with a slope of -3
y +1 = -3 (x-2)
The perimeter of a rectangle is 38 cm. The length is 3 cm more than twice the width. Find the dimensions
width = 4cm
length = 11cm
A line passes through (2,5) and (6,13). Find its equation in y=mx+b
y = 2x +1
Solve by elimination:
2x+y=7
3x−y=8
(3, 1)
Two parallel lines are cut by a transversal. If a corresponding angle measures 112 degrees, what is the measure of the alternate interior angle?
112
Find the distance between (1,2) and (7,10)
10
Solve (2x-3)/5 = (x+4)/2
x = -26
A function has slope −1/2 and passes through (8,−1). Write its equation.
y = -1/2x + 3
Determine whether the system has one solution, no solution, or infinitely many solutions:
2x+4y=10
x+2y=5
infinite solutions
Two same-side interior angles measure (3x+5) and (5x−9). Find x
x = 23
Determine whether the lines through (1,2),(5,10) and (−2,6),(1,0) are parallel, perpendicular, or neither.
perpendicular
A taxi charges a $4 flat fee plus $2.75 per mile. Another company charges $7 plus $2.25 per mile. At what distance do the costs equal?
6 miles
A function has x-intercept 6 and y-intercept –4. Write its equation
y = 2/3x - 4
A school sells adult tickets for $8 and student tickets for $5. A total of 140 tickets were sold for $910. How many of each ticket were sold?
42 adult tickets and 98 student tickets
Two parallel lines are cut by a transversal. One angle is labeled (4x+18) and its alternate interior angle is labeled (7y−3). The angle adjacent to the second angle is labeled (2x+y+15). Find the values of x and y
x = 17, y = 13
Points A(−4,1), B(2,5), and C(6,−1) are three vertices of a quadrilateral ABCD.
Determine the coordinates of point D so that ABCD is a parallelogram.
(0, -5)