Lesson 2 Homework Practice Slope Answer Key

Lesson 2 Homework Practice: Slopes of Lines

In this lesson, you will learn how to find the slope of a line given two points or a graph. The slope of a line is a measure of how steep or slanted the line is. The slope can be positive, negative, zero, or undefined. The slope can also be used to write the equation of a line or to determine if two lines are parallel or perpendicular.

Lesson 2 Homework Practice Slope Answer Key

The slope of a line can be calculated using the formula:

where m is the slope, and (x1, y1) and (x2, y2) are two points on the line.

For example, to find the slope of the line passing through the points (3, 5) and (6, 11), we can plug in the coordinates into the formula:

The slope of this line is 2, which means that for every unit increase in x, the y value increases by 2 units. This is a positive slope, which means that the line goes up from left to right.

To find the slope of a line from a graph, we can use the same formula, but we need to identify two points on the line and their coordinates. For example, to find the slope of the line shown below, we can choose any two points on the line, such as A and B:

The coordinates of point A are (0, 4) and the coordinates of point B are (4, 0). Plugging these into the formula, we get:

The slope of this line is -1, which means that for every unit increase in x, the y value decreases by 1 unit. This is a negative slope, which means that the line goes down from left to right.

Sometimes, the slope of a line can be zero or undefined. A zero slope means that the line is horizontal and has no change in y. An undefined slope means that the line is vertical and has no change in x. For example, the graph below shows two lines with zero and undefined slopes:

The blue line has a zero slope because it is horizontal and has a constant y value of 2. The red line has an undefined slope because it is vertical and has a constant x value of -3.

The slope of a line can also be used to write the equation of a line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the line crosses the y-axis. For example, if we know that a line has a slope of 2 and passes through the point (3, 5), we can use these information to find the y-intercept and write the equation of the line:

The equation of this line is y = 2x - 1. c481cea774