Questions and Answers
What is slope-intercept form for the equation of a line?
y=mx+b
The b in y=mx+b is the?
y-intercept (where the line crosses the y-axis)
The m in the y=mx+b is the?
slope of the line (rise over run)
What is the slope formula?
Signup and view all the answers
Give an example of undefined slope.
Signup and view all the answers
Give an example of zero slope.
Signup and view all the answers
Give an example of positive slope.
Signup and view all the answers
Give an example of negative slope.
Signup and view all the answers
Write the equation if b = 3 and m = -2.
Signup and view all the answers
Write the equation if b = -7 and m = 1/2.
Signup and view all the answers
What does the graph of y = -3/2x + 3 look like?
Signup and view all the answers
To write the equation of a line, you need to find what?
Signup and view all the answers
What is the Y-intercept?
Signup and view all the answers
What is the slope of a horizontal line?
Signup and view all the answers
What is the slope of a vertical line?
Signup and view all the answers
What is the y-intercept of a vertical line?
Signup and view all the answers
At what point do you start graphing the line y=x?
Signup and view all the answers
How do you count the slope for the line y=x?
Signup and view all the answers
What is the equation for a horizontal line that goes through 5?
Signup and view all the answers
What is the equation for a vertical line that goes through 5?
Signup and view all the answers
What happens when you subtract a negative?
Signup and view all the answers
What does -3/-6 simplify down to?
Signup and view all the answers
Study Notes
Slope-Intercept Form
- Slope-intercept form is represented by the equation y = mx + b.
- m indicates the slope, calculated as the rise over the run.
- b represents the y-intercept, where the line intersects the y-axis.
Slope Formulas and Characteristics
- Slope formula measures the steepness of a line.
- Undefined slope occurs with vertical lines; there is no defined slope for these lines.
- Zero slope occurs with horizontal lines; these lines maintain a constant y-value.
- Positive slope indicates an upward trend as you move along the x-axis, while negative slope shows a downward trend.
Graphing Lines
- To construct a line’s equation, you must determine the slope (m) and y-intercept (b).
- The y-intercept is the coordinate point where the line intersects the y-axis.
- For the line y = x, begin graphing at the origin (0,0) and move up one unit and right one unit to plot points.
Equations of Specific Lines
- A horizontal line passing through y = 5 is represented as y = 5.
- A vertical line passing through x = 5 is written as x = 5.
Special Cases
- y = -3/2x + 3 generates a line with a negative slope and a y-intercept of 3.
- The equation derived from values b = 3 and m = -2 is y = -2x + 3.
- When b = -7 and m = 1/2, the equation is y = 1/2x - 7.
Simplification and Operations
- Subtracting a negative number equates to adding that number.
- The fraction -3/-6 simplifies to 1/2.
Key Points
- The slope of a horizontal line is always 0.
- A vertical line's slope is deemed undefined.
- A vertical line does not possess a y-intercept at any point.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of the slope-intercept form, y=mx+b, with these flashcards designed for Algebra 1. Each card includes key terms such as the slope and y-intercept, along with their definitions. Perfect for reinforcing your understanding of linear equations.