Writing Linear Equations

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 identify the slope from the equation y = -2x + 5?

Back

The slope is -2.

Front

What does the y-intercept represent in the equation y = mx + b?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

How can you convert the equation 5x - 2y = 12 to slope-intercept form?

Back

To convert to slope-intercept form, solve for y: y = (5/2)x - 6.

Front

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

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How do you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to plot another point.

Front

What is the relationship between parallel lines in terms of slope?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between perpendicular lines in terms of slope?

Back

Perpendicular lines have slopes that are negative reciprocals of each other.

Front

How do you determine 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 to write the equation.