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 determine the slope from a graph?

Back

The slope is determined by the rise over run, which is the change in y divided by the change in x between two points on the line.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

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

Back

Use the formula for slope (m = (y2 - y1) / (x2 - x1)) to find the slope, then use point-slope form (y - y1 = m(x - x1)) to write the equation.

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph.

Front

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

Back

Identify the pattern in the changes of y with respect to x, determine the slope, and use a point to find the y-intercept.

Front

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

Back

The coefficients indicate the slope and the y-intercept, which determine the steepness and position of the line.

Front

What does it mean if a line has a negative slope?

Back

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

Front

How can you verify if an equation matches a graph?

Back

Substitute values from the graph into the equation to see if the resulting y-values match the corresponding x-values.

Front

What is the difference between positive and negative slopes?

Back

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