Writing Equations Given a Graph, Table, or Two Points

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line in slope-intercept form (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x is 0. It is represented by 'b' in the slope-intercept form of a linear equation.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the equation y = mx + b represent?

Back

This is the slope-intercept form of a linear equation, where 'm' is the slope and 'b' is the y-intercept.

Front

How can you determine if a function is linear from a graph?

Back

A function is linear if its graph is a straight line. The slope remains constant between any two points on the line.

Front

What is the relationship between the slope and the direction of a line?

Back

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

Front

If a line has a slope of -3, what does this indicate about its steepness?

Back

A slope of -3 indicates a steep decline; for every 1 unit increase in x, y decreases by 3 units.

Front

How do you write an equation from two points?

Back

1. Calculate the slope (m) using the two points. 2. Use one point to find the y-intercept (b). 3. Write the equation in the form y = mx + b.

Front

What is the significance of the x-intercept in a linear equation?

Back

The x-intercept is the value of x when y is 0. It indicates where the line crosses the x-axis.

Front

What does the term 'linear relationship' mean?

Back

A linear relationship means that there is a constant rate of change between two variables, represented by a straight line on a graph.