Math Skills – Linear Equations (Day 1) Flashcards
What is a linear equation?
An equation that models a straight line, typically written as y = mx + b, where m is the slope and b is the y-intercept.
What does m represent in y = mx + b ?
The slope of the line, which indicates the rate of change or steepness.
What does b represent in y = mx + b?
The y-intercept, where the line crosses the y-axis.
How do you solve 3x + 4 = 10?
Subtract 4 from both sides: 3x = 6.
Divide by 3: x = 2.
What does it mean when a line has a slope of 0?
The line is horizontal.
How do you find the slope between two points (x_1, y_1) and (x_2, y_2)?
Use the formula m = {y_2 - y_1}/{x_2 - x_1}.
What is the graph of a linear equation?
A straight line that represents all solutions to the equation.
How do you graph y = 2x + 1 ?
Start at the y-intercept (b = 1), then use the slope (m = 2) to plot additional points (e.g., go up 2 units, right 1 unit).
What happens when you increase the slope in y = mx + b?
The line becomes steeper.
What happens when you change the y-intercept in y = mx + b?
The line shifts up or down without changing its slope.
What does it mean if two lines have the same slope?
They are parallel.
How do you know if two lines are perpendicular?
Their slopes are negative reciprocals. For example, if one slope is m = 2, the other must be m = - {1}/{2}.
What is a function?
A relation where each input (x) has exactly one output (y).
How do you determine if a graph represents a function?
Use the vertical line test. If a vertical line intersects the graph more than once, it’s not a function.
How can linear equations be used in real life?
To model relationships such as distance over time, cost versus quantity, or temperature changes.
In the equation y = 5x + 20, what does the 20 represent in a real-world context?
The initial value or starting point.
In the equation y = 5x + 20, what does the 5 represent in a real-world context?
The rate of change or how much y increases for each unit increase in x.
What are the four quadrants on a graph?
• Quadrant I: (+x, +y)
• Quadrant II: (-x, +y)
• Quadrant III: (-x, -y)
• Quadrant IV: (+x, -y)
How do you plot the point (3, -2) on a graph?
Move 3 units to the right on the x-axis and 2 units down on the y-axis.
What is the origin on a graph?
The point (0, 0), where the x-axis and y-axis intersect.
