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 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

Given the points (2, 3) and (4, 7), write the equation of the line in slope-intercept form.

Back

The slope is m = (7 - 3) / (4 - 2) = 2. The equation is y = 2x - 1.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.

Front

How can you determine if a point (x, y) lies on a line represented by the equation y = mx + b?

Back

Substitute the x-value into the equation to see if the resulting y-value matches the y-coordinate of the point.

Front

What is the significance of the coefficient of x in the equation y = mx + b?

Back

The coefficient of x (m) represents the slope of the line, indicating how steep the line is.

Front

If a table shows values of x and y, how can you find the equation of the line?

Back

Identify two points from the table, calculate the slope, and use one point to find the y-intercept.

Front

What is the formula to convert a table of values into a linear equation?

Back

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

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.