Holt CA Course Finding Slope of a Line AF3.4 Plot the values of quantities whose ratios are always the same (e.g. cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. Also covered: AF3.3. California Standards

Holt CA Course Finding Slope of a Line Recall that lines have constant slope. For a line on the coordinate plane, slope is the following ratio: vertical change horizontal change change in y change in x =

Holt CA Course Finding Slope of a Line If you know any two points on a line, you can find the slope of the line without graphing. The slope of a line through the points (x 1, y 1 ) and (x 2, y 2 ) is as follows: y2 – y1y2 – y1x2 – x1x2 – x1y2 – y1y2 – y1x2 – x1x2 – x1 When finding slope using the ratio above, it does not matter which point you choose for (x 1, y 1 ) and which point you choose for (x 2, y 2 ). slope =

Holt CA Course Finding Slope of a Line Find the slope of the line that passes through A. (–2, –3) and (4, 6). Additional Example 1: Finding Slope, Given Two Points Let (x 1, y 1 ) be (–2, –3) and (x 2, y 2 ) be (4, 6). 6 – (–3) 4 – (–2) Substitute 6 for y 2, –3 for y 1, 4 for x 2, and –2 for x = The slope of the line that passes through (–2, –3) and (4, 6) is. 3 2 = y 2 – y 1 x 2 – x = Simplify. 3 2 =

Holt CA Course Finding Slope of a Line Find the slope of the line that passes through B. (1, 3) and (2, 1). Additional Example 1: Finding Slope, Given Two Points Let (x 1, y 1 ) be (1, 3) and (x 2, y 2 ) be (2, 1). 1 – 3 2 – 1 Substitute 1 for y 2, 3 for y 1, 2 for x 2, and 1 for x 1. 22 1 = The slope of the line that passes through (1, 3) and (2, 1) is –2. = y 2 – y 1 x 2 – x 1 = –2 Simplify.

Holt CA Course Finding Slope of a Line Find the slope of the line that passes through C. (3, –2) and (1, –2). Additional Example 1: Finding Slope, Given Two Points Let (x 1, y 1 ) be (3, –2) and (x 2, y 2 ) be (1, –2). –2 – (–2) 1 – 3 Substitute 2 for y 2, 2 for y 1, 1 for x 2, and 3 for x 1.  – 3 = The slope of the line that passes through (3, –2) and (1, –2) is 0. = y 2 – y 1 x 2 – x 1 = 0 Rewrite subtraction as addition of the opposite. 0 –2 =

Holt CA Course Finding Slope of a Line Find the slope of the line that passes through A. (–4, –6) and (2, 3). Check It Out! Example 1 Let (x 1, y 1 ) be (–4, –6) and (x 2, y 2 ) be (2, 3). 3 – (–6) 2 – (–4) Substitute 3 for y 2, –6 for y 1, 2 for x 2, and –4 for x = The slope of the line that passes through (–4, –6) and (2, 3) is. 3 2 = y 2 – y 1 x 2 – x =

Holt CA Course Finding Slope of a Line Find the slope of the line that passes through B. (2, 4) and (3, 1). Check It Out! Example 1 Let (x 1, y 1 ) be (2, 4) and (x 2, y 2 ) be (3, 1). 1 – 4 3 – 2 Substitute 1 for y 2, 4 for y 1, 3 for x 2, and 2 for x 1. 33 1 = The slope of the line that passes through (2, 4) and (3, 1) is –3. = y 2 – y 1 x 2 – x 1 = –3 Simplify.

Holt CA Course Finding Slope of a Line Find the slope of the line that passes through C. (3, –2) and (1, –4). Check It Out! Example 1 Let (x 1, y 1 ) be (3, –2) and (x 2, y 2 ) be (1, –4). –4 – (–2) 1 – 3 Substitute 4 for y 2, 2 for y 1, 1 for x 2, and 3 for x 1. – – 3 = The slope of the line that passes through (3, –2) and (1, –4) is –2. = y 2 – y 1 x 2 – x 1 Simplify. = 1 –2 =

Holt CA Course Finding Slope of a Line Additional Example 2: Money Application The table shows the total cost of fruit per pound purchased at the grocery store. Use the data to make a graph. Find the slope of the line and explain what it shows. Graph the data. Pounds Cost Cost of Fruit

Holt CA Course Finding Slope of a Line You can use any two points to find the slope of the line. Helpful Hint

Holt CA Course Finding Slope of a Line Additional Example 2 Continued Find the slope of the line: The slope of the line is 3. This means that for every pound of fruit, you will pay another $3. y 2 – y 1 x 2 – x   5 = 3 Pounds Cost Cost of Fruit Substitute Multiply

Holt CA Course Finding Slope of a Line Check It Out! Example 2 The table shows the total cost of gas per gallon. Use the data to make a graph. Find the slope of the line and explain what it shows. Graph the data. Cost of Gas GallonsCost x y Gallons Cost of Gas Cost

Holt CA Course Finding Slope of a Line Check It Out! Example 2 Continued Find the slope of the line: The slope of the line is 2. This means that for every gallon of gas, you will pay another $2. = y 2 – y 1 x 2 – x  6 6  3 = x y Gallons Cost of Gas Cost Substitute. Multiply.

Holt CA Course Finding Slope of a Line The slope of a line may be positive, negative, zero, or undefined. You can tell which of these is the case by looking at the graphs of a line— you do not need to calculate the slope.

Holt CA Course Finding Slope of a Line

Holt CA Course Finding Slope of a Line