Slope-Intercept Form
Write the slope-intercept form of a line.
y=mx+by=mx+b where m is the slope and b is the y-intercept.
What point is the y-intercept of the line y=−x+2?
y-intercept is (0,2).
What does the intersection point of two lines represent when solving a system by graphing?
The intersection point is the solution to the system — the ordered pair (x,y) that satisfies both equations.
Identify the slope and y-intercept of the line y=3x−5.
slope =3,
y-intercept = -5
(0,−5)(0,−5)
If a line has slope 0, what does it look like?
It's a horizontal line.
Solve the system by graphing conceptually: y=x+2 and y=x−1. (Do they intersect? If so, where?)
They do not intersect; there is no solution (no solution / inconsistent system).
A line has slope −2/3 and y-intercept (0,4). Write its equation.
y= -2/3x+4.
Given the equation y=−3/2x+3:
Calculate two ordered pairs that satisfy the equation.
(0,3)
(2,0)
Rewrite the equation in slope-intercept form.
2x+y=4
y=-2x+4
Convert the equation 2x−4y=8 to slope-intercept form and state the slope.
y=1/2x−2
slope=1/2
Determine whether the line through points (2,3) and (5,9) has a slope of positive, negative, zero, or undefined. Show the slope calculation.
Positive slope (specifically m=2).
Determine whether the system has one solution, no solution, or infinitely many: y=3x+2 and 3x+2y=−4.
Exactly one solution (the lines intersect at a single point).
The graph of a line passes through (-1,2) and has slope 5/4. Find the equation in slope-intercept form.
y=5/4x+13/4.
Given two lines: y=2x+1 and y=2x−3. Describe their slopes and y-intercepts and explain how their graphs relate to each other.
Both lines have the same slope m=2m=2, different y-intercepts (1 and −3). They are parallel lines and do not intersect.
Solve the system and explain the result (one solution, no solution, or infinitely many):
y = −(1/3)x + 4
2x + 6y = 12
The system has no solution.