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

The slope (m) represents the rate of change of the line, indicating how steep the line is and the direction it goes (positive or negative).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope 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 is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

If a line has a slope of -5/3, what does this indicate about its direction?

Back

A slope of -5/3 indicates that the line is decreasing; for every 3 units you move to the right, the line goes down 5 units.

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, indicating the value of x when y = 0.

Front

How can 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 (y = mx + b), solve for y.

Front

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

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).