1. What is a linear equation?
- A linear equation is an equation that forms a straight line when graphed. It can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept.
2. How do you determine the slope and y-intercept of a linear equation?
- The slope (m) of a linear equation can be found by comparing the change in y-values with the change in x-values, often written as (y2 - y1) / (x2 - x1) for two points on the line. The y-intercept (b) is the point where the line intersects the y-axis, often represented as (0, b).
3. What is the general process for graphing a linear equation?
- To graph a linear equation, start by plotting the y-intercept on the y-axis. Then, use the slope to find a second point on the line, and connect the two points with a straight line.
4. Can a linear equation have more than one solution?
- No, a linear equation has only one solution, represented by the line on the graph.
5. What does the slope of a linear equation represent?
- The slope of a linear equation represents the rate of change of the line. A positive slope indicates an upward trend, while a negative slope indicates a downward trend.
6. How can you check if a point lies on a linear equation?
- To check if a point lies on a linear equation, substitute the x and y-values of the point into the equation and see if the equation holds true. If it does, then the point lies on the line.
7. Can a linear equation have a slope of zero? What would the graph look like?
- Yes, a linear equation can have a slope of zero, which means the line would be horizontal. The graph would be a straight line parallel to the x-axis.
Lesson 12 graphing linear equations review
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