Writing Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does slope represent in a linear equation?

Back

Slope represents the steepness of the line and the direction it goes. It is calculated as the change in y divided by the change in x (rise over run).

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

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

Back

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

Front

Write the equation of a line with a slope of 2 and a y-intercept of 3.

Back

y = 2x + 3.

Front

What is the equation of a line that passes through the points (1, 2) and (3, 4)?

Back

The equation is y = x + 1.

Front

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

Back

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

Front

What is the significance of the x-intercept in a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, and it can be found by setting y = 0 in the equation.

Front

If a line has a slope of -3, what does this indicate about its direction?

Back

A slope of -3 indicates that the line is decreasing; as x increases, y decreases.