Writing equations from tables and graphs

Front

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

Back

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

Front

How do you find the slope from a table of values?

Back

The slope (m) can be found by taking the difference in y-values divided by the difference in x-values (m = (y2 - y1) / (x2 - x1)).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

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

Back

Identify two points on the line, calculate the slope, and use one point to find the y-intercept, then write the equation in slope-intercept form.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning that y remains constant regardless of the value of x.

Front

How do you convert a table of values into a linear equation?

Back

Identify the slope from the table, find the y-intercept, and then write the equation in the form y = mx + b.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, indicating they intersect at a right angle.