LINEAR EQUATIONS
What is the slope of the line represented by the equation y=5x+3?
5
Find the slope between the points (1,2) and (3,6).
m= 4/2 = 2
What is a "system of equations"?
Two or more equations with the same variables.
Solve
y = 2x and x + y = 12
(4,8)
What do you call the steepness of a line?
Slope
Write the equation of a line that passes through (0, 2) with a slope of -4.
y=−4x+2
What type of slope does a horizontal line have?
0 slope
How many solutions does a system have if the lines are parallel?
No solution
Solve using substitution
y = x - 5 and
2x + y = 1
(2,-3)
What is the point where a graph crosses the y-axis called?
In the graphed line: y=−2x+1 What is the y-intercept?
1
Find the slope between (-2, 5) and (4, 5).
0
Solve the system:
y = 2x + 1 and y = -x + 7
A) (2, 5)
B) (1, 3)
C) (3, 7)
D) (5, 11)
A) (2,5)
Solve:
y=3x and 2x+y=10
(2,6)
What form is the equation y=mx+by=mx+b called?
Slope-intercept form
Rewrite 3x−2y=6 in slope-intercept form.
y = 3/2x - 3
Find the slope between the points (4, 2) and (4, -3).
-5
A system has infinitely many solutions. What does that mean about the two lines?
They are the same line.
Solve:
x = y + 2 and x - 3y = -4
(2,0)
What kind of lines have no solution when solving a system?
Parallel Lines
A line has a slope of 3 and passes through (2, -1). Write the equation in point-slope form.
y+1=3(x−2)
Which slope is steeper: -2 or 5?
5
2x + 3y = 12
4x + 6y = 24
What is true about these equations?
A. They are the same line (infinitely many solutions)
B. They are parallel and do not intersect ( no solution)
C. They intersect at one point ( one solution)
A. They are the same line (infinitely many solutions)
Solve:
y = 4x -3 and
2x + y = 5
(2,5)
What does it mean when a system has "one solution"?