Unit 4 Alg Flashcardizz slope and graphing

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you find the y-intercept of a linear equation in slope-intercept form?

Back

In the slope-intercept form of a linear equation, y = mx + b, the y-intercept is the value of b, which is the point where the line crosses the y-axis.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How can you convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What does the slope of a line indicate about its direction?

Back

A positive slope indicates that the line rises from left to right, while a negative slope indicates that the line falls from left to right.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is significant because it indicates the value of y when x is zero, providing a starting point for the graph of the linear equation.

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then divide the rise by the run.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope, meaning they rise and run at the same rate, and will never intersect.

Front

What is the relationship between perpendicular lines and their slopes?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one line has a slope of m, the other will have a slope of -1/m.

Front

How can you identify the correct graph for a given linear equation?

Back

To identify the correct graph for a linear equation, determine the slope and y-intercept, then plot the y-intercept and use the slope to find another point on the line.