Writing Equations Given a Graph, Table, or Two Points

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope (m) 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 y-intercept (b) represent in the equation y = mx + b?

Back

The y-intercept (b) represents the point where the line crosses the y-axis.

Front

If a line has a slope of -1/2, what does this indicate about its direction?

Back

A slope of -1/2 indicates that for every 2 units you move to the right, the line moves down 1 unit.

Front

What is the relationship between the variables in the equation d = 10t?

Back

This equation indicates that distance (d) is directly proportional to time (t) with a constant of proportionality of 10.

Front

How can you determine the equation of a line from a graph?

Back

To determine the equation, identify the slope and y-intercept from the graph, then use the slope-intercept form y = mx + b.

Front

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

Back

The x-value represents the independent variable, which can be changed to find corresponding y-values.

Front

What does it mean if two points lie on a vertical line?

Back

If two points lie on a vertical line, it means that they have the same x-coordinate, indicating an undefined slope.

Front

How do you write an equation from a table of values?

Back

Identify the pattern in the changes of y-values relative to x-values, then use the slope and y-intercept to form the equation.

Front

What is the formula for finding the y-value when given an x-value in a linear equation?

Back

Substitute the x-value into the equation y = mx + b to find the corresponding y-value.