Determining Slope and Y-Intercept

Warm Up 3. Find the slope and the y-intercept of the line represented by the table.

Introduction to the slope-intercept form of a linear equation. Determine the slope and y-intercept of linear equations from tables and from graphs. Determine the rate of change of a linear relationship. Determine the initial value of a linear relationship. Use the slope-intercept form of an equation of a line. Derive the slope-intercept form of a linear equation. Relate the slope to the rate of change and the y-intercept to the initial value of the linear relationship. This is in preparation for graphing linear relationships using the slope and the y-intercept.

Find the slope of a line that passes through the points (-4, -2) and (4, 2). Remember that the slope is the rise over the run or the change in x over the change in y.

How can you determine the slope and the y-intercept of a line How can you determine the slope and the y-intercept of a line? Find the slope of the line using the coordinates of two points found on the graph. Then find the y-coordinate of the point where the graph crosses the y-axis.

Remember that to find the ratio of the change in y over the change in x to find the slope, m. Don’t just divide the first value of y by the corresponding value of x to find the slope. In order to find the y-intercept, work backward to find the y-value when x is 0.

Horizontal lines have a slope of 0 since the rise is 0 for any run, and 0 divided by a nonzero number is 0. Therefore, an equation for a horizontal line takes the form y = b, where b is the y-intercept. The slope of a vertical line is undefined because any two points on the line will have a run of 0, and division by 0 is undefined. A vertical line also has no y-intercept, unless it passes through the origin, in which case the line contains all points on the y-axis.

Gregg deposits the money he makes from mowing lawns into his savings account, adding it to the money his father gave him to open the account. Confirm the relationship is linear and give the constant rate of change and the initial value.

Compare the slopes and y-intercepts of two lines with the equations y = 2x + 3 and y = 2x + 5.

How can you determine the slope and y-intercept of a line represented by a table? Find the constant rate of change, which is the slope. Find the initial value, y when x = 0 from the table, or work backward to find it. This value will be the y-intercept.

Some carpet cleaning costs are shown in the table Some carpet cleaning costs are shown in the table. The relationship is linear. Find and interpret the rate of change and the initial value for this situation.

John has a job parking cars John has a job parking cars. He earns a fixed weekly salary of $300 plus a fee of $5 for each car he parks. His potential earnings for a week are shown in the graph. At what point does John begin to earn more from fees than his fixed salary? Justify your answer.

Exit Ticket 2. Find and interpret the rate of change. 3. Find and interpret the initial value. 4. After how many minutes will the barrel be empty? Explain.