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 a linear equation in slope-intercept form?

Back

The slope (m) is the coefficient of x in the equation y = mx + b.

Front

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

Back

The y-intercept (b) represents 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 given two points?

Back

To determine the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to find the equation.

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 as x increases.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

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, indicating a constant rate of change.

Front

What is the formula for finding the y-intercept from a linear equation?

Back

To find the y-intercept from a linear equation in standard form Ax + By = C, set x = 0 and solve for y.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept (b), plot it on the y-axis, then use the slope (m) to find another point by rising and running from the y-intercept.

Front

What is the relationship between the coefficients of a linear equation and its graph?

Back

The coefficients of a linear equation determine the slope and y-intercept, which define the steepness and position of the line on the graph.