Coordinate Plane
The point (-4, -12) is located in which quadrant?
Quadrant III
What is the equation of a horizontal line passing through (0, -3)?
y = -3
What is the formula for finding slope from two points?
m = (y₂ - y₁)/(x₂ - x₁)
Use the distributive property to rewrite -3(x - 4) = 17 without parentheses.
-3x + 12 = 17
Which point is on the graph of 5x + 2y = 10? Choices: (2, 5), (5, 2), (2, 0), (0, 2)
(2, 0)
The graph of y = 2 makes what kind of line?
A horizontal line.
Does the graph of 4x + y = 6 slope upward, slope downward, or form a horizontal or vertical line?
It slopes downward. In slope-intercept form, y = -4x + 6
Write an equation in slope-intercept form for a line with slope = -3 and y-intercept (0,5)
y=-3x+5
Solve: 4(-x + 7) = 12
x = 4
Solve: |2x - 5| = 9
x = 7 or x = -2
What are the x-intercept and y-intercept of 4x - 8y = 2?
x-intercept: (1/2, 0); y-intercept: (0, -1/4)
What is the slope of 3x - 6y = 2?
1/2
Write the equation of a line with slope 2 passing through (-1, -1).
y = 2x + 1
When solving a linear equation, what is the goal, and how do you accomplish it?
Isolate the variable using inverse operations and properties of equality while keeping both sides balanced.
Which point is a solution to y = (3/4)x + 2? Choices: (0, -2), (4, -1), (-4, -1), (4, 4)
(-4, -1)
Does the point (3,-2) satisfy 2x+3y=0? Explain.
Yes. 2(3)+3(-2)=6-6=0
What is the x-intercept of y = (1/4)x - 1?
(4, 0)
Two parts: (1) How many distinct points are necessary to graph a line? (2) How many solutions does a linear equation in two variables representing a line have?
(1) Two distinct points. (2) Infinitely many solutions
Solve: 2 - 3x = -4 + 3x
x = 1
Solve: 3x + 5 ≤ 2x - 7
x ≤ -12
Find both intercepts of 3x+4y=24
x-intercept: (8,0); y-intercept: (0,6)
Rewrite 6x-3y=12 in slope-intercept form. State the slope and y-intercept.
y=2x-4; slope = 2; y-intercept (0,-4)
Rewrite y - 10 = -5(x + 3) in slope-intercept form and standard form.
Slope-intercept: y = -5x - 5. Standard: 5x + y = -5
Solve: 5(x - 4) = 2x + 7
x = 9
Solve: |x - 4| > -6
All real numbers.