Writing Linear Equations from Graph

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 the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept (b) in a linear equation?

Back

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

Front

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

Back

The slope (m) can be 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

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 equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.

Front

If a line has a slope of -1/2, what does this indicate about the line's direction?

Back

A slope of -1/2 indicates that for every 2 units the line moves to the right, it moves down 1 unit, showing a downward direction.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is y = b, where b is the y-value for all points on the line.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is x = a, where a is the x-value for all points on the line.