Point-Slope Form Section 5-4 Part 2

Goals Goal To write and graph linear equations using point-slope form. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

Vocabulary None

Point-Slope Form Point-Slope Form can also be used to write the equation of a line given two points. Procedure 1)Use the two given points to calculate the slope. 2)Substitute the slope and one of the given points into the point-slope form. 3)Rewrite equation in slope-intercept form if required.

Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point- slope form. Choose (2, –3). y – y 1 = m(x – x 1 ) y – (–3) = 2(x – 2) Example: Write Equation of Line Given Two Points

Step 3 Write the equation in slope-intercept form. y = 2x – 7 –3 y + 3 = 2(x – 2) y + 3 = 2x – 4 Example: Continued y – (–3) = 2(x – 2)

Write an equation in slope-intercept form for the line through the two points. (0, 1) and (–2, 9) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point- slope form. Choose (0, 1). y – y 1 = m(x – x 1 ) y – 1 = –4(x – 0) Example: Write Equation of Line Given Two Points

Step 3 Write the equation in slope-intercept form. y = –4x y – 1 = –4(x – 0) y – 1 = –4x Example: Continued y – 1 = –4(x – 0)

Write an equation in slope-intercept form for the line through the two points. (1, –2) and (3, 10) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point- slope form. Choose (1, –2). y – y 1 = m(x – x 1 ) y – (–2) = 6(x – 1) y + 2 = 6(x – 1) Your Turn:

Step 3 Write the equation in slope-intercept form. y + 2 = 6x – 6 – 2 y = 6x – 8 y + 2 = 6(x – 1) Continued

Write an equation in slope-intercept form for the line through the two points. (6, 3) and (0, –1) Step 1 Find the slope. Step 2 Substitute the slope and one of the points into the point- slope form. Choose (6, 3). y – y 1 = m(x – x 1 ) Your Turn:

Step 3 Write the equation in slope-intercept form Continued

The cost to stain a deck is a linear function of the deck’s area. The cost to stain 100, 250, 400 square feet are shown in the table. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet. Example: Application

Understand the Problem1 The answer will have two parts—an equation in slope- intercept form and the cost to stain an area of 75 square feet. The ordered pairs given in the table—(100, 150), (250, ), (400, 525)—satisfy the equation. Example: Continued

2 Make a Plan You can use two of the ordered pairs to find the slope. Then use point-slope form to write the equation. Finally, write the equation in slope-intercept form. Example: Continued

Solve Step 1 Choose any two ordered pairs from the table to find the slope. Use (100, 150) and (400, 525). Step 2 Substitute the slope and any ordered pair from the table into the point-slope form. y – 150 = 1.25(x – 100) Use (100, 150). y – y 1 = m(x – x 1 ) Example: Continued

Step 3 Write the equation in slope-intercept form by solving for y. y – 150 = 1.25(x – 100) y – 150 = 1.25x – 125 Distribute y = 1.25x + 25 Add 150 to both sides. Step 4 Find the cost to stain an area of 75 sq. ft. y = 1.25x + 25 y = 1.25(75) + 25 = The cost of staining 75 sq. ft. is $ Example: Continued

At a newspaper the costs to place an ad for one week are shown. Write an equation in slope-intercept form that represents this linear function. Then find the cost of an ad that is 21 lines long. Your Turn:

Step 1 Choose any two ordered pairs from the table to find the slope. Use (3, 12.75) and (5, 17.25). Step 2 Substitute the slope and any ordered pair from the table into the point-slope form. Use (5, 17.25). y – y 1 = m(x – x 1 ) y – = 2.25(x – 5) Solution:

Step 3 Write the equation in slope-intercept form by solving for y. y – = 2.25(x – 5) y – = 2.25x – Distribute y = 2.25x + 6 Add to both sides. Step 4 Find the cost for an ad that is 21 lines long. y = 2.25x + 6 y = 2.25(21) + 6 = The cost of the ad 21 lines long is $ Continued

Joke Time What does a ghost wear when it’s raining outside? Booooooooooooooooooots! What do you call it when a dinosaur crashes his car? Tyrannosaurus Wrecks! Why are all the frogs around here dead? Because they keep croaking.

Assignment 5-4 Part 2 Exercises Pg : #4 – 22 even