Linear equations 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 (upward or downward).

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 is the value of y when x = 0.

Front

How do you graph the equation y = 2x - 4?

Back

1. Start at the y-intercept (0, -4). 2. Use the slope (2) to rise 2 units and run 1 unit to the right. 3. Draw the line through these points.

Front

What is the graph of x = 1?

Back

The graph of x = 1 is a vertical line that crosses the x-axis at the point (1, 0).

Front

How do you identify the equation of a line from its graph?

Back

Look for the slope and y-intercept. Use the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the equation y = -2x + 4 represent?

Back

This equation represents a line with a slope of -2 and a y-intercept of 4. It decreases as x increases.

Front

What is the graph of y = -4?

Back

The graph of y = -4 is a horizontal line that crosses the y-axis at the point (0, -4).

Front

How do you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the significance of the point (0, b) in a linear equation?

Back

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