Write Linear Equations From Tables

Front

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

Back

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

Front

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

Back

To determine the slope from a table of values, calculate the change in y (rise) divided by the change in x (run) between two points.

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

How can you write a linear equation from a table of values?

Back

To write a linear equation from a table, identify the slope and y-intercept from the values, then use the slope-intercept form.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change of y with respect to x; a positive slope means y increases as x increases, while a negative slope means y decreases.

Front

If a table shows a constant rate of change, what type of relationship does it represent?

Back

A constant rate of change in a table represents a linear relationship.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, first calculate the slope using the formula (y2 - y1) / (x2 - x1), then use one of the points and the slope to write the equation in point-slope form or slope-intercept form.

Front

What is point-slope form of a linear equation?

Back

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

Front

How can you convert an equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What does it mean if a linear equation has a slope of zero?

Back

A linear equation with a slope of zero represents a horizontal line, indicating that y does not change as x changes.