Warm Up Solve each equation for y. 1. 4x + 2y = 10 2. 3x + 2 = 6y y = –2x + 5 3. Find the slope of the line that contains (5, 3) and (–1, 4). Find the slope of the line. 4. m = ½ Write an equation of a line in point-slope form, then rewrite in slope-intercept form. y – 2 = 2(x – 1) y = 2x y – 3 = -4(x + 2) y = -4x + 5 5. m = 2; (1, 2) 6. m = -4; (-2, 3)

Linear Equations Slope (Rate of Change) Slope-Intercept Form Point-Slope Form Standard Form

Slope is a number usually a fraction that tells how a line slants comes in 4 “flavors”: positive, negative, zero, undefined

Slope Slope is abbreviated with a lower case letter m. Is a number Usually a fraction That tells how a line slants Slope is abbreviated with a lower case letter m.

Find the slope of a line using a graph: Step 1 Pick two “nice” points on the line. Students should follow along on their handout, filling in blanks as needed.

Find the slope of a line using a graph: Step 2 Use the two points to draw a right triangle. Make sure that the line is the hypotenuse!

Find the slope of a line using a graph: Step 3 Find the rise (vertical change) and run (horizontal change) of the line. Run = 3 Rise = 2 Slope is like a baby – it has to rise (stand) before it can run!

Find the slope of a line using a graph: Step 4 Write the slope as a fraction Rise Run Make sure you include a – sign if it is a negative slope! Run = 3 Rise = 2 Slope 2 3

Using the Slope Formula: Display one problem at a time. Have students find the answer mentally, then reveal the answer. Using the Slope Formula:

Find the slope of the line that passes through the points (-2,-5) and (4,3). x1, y1 x2, y2 First: Label the ordered pairs: (-2, -5) and (4, 3). Second: Use the formula to find the slope. What do you think?

Remember that slope is a rate of change Remember that slope is a rate of change. In real-world problems, finding the slope can give you information about how a quantity is changing.

Any linear equation can be written in slope-intercept form by solving for y and simplifying. In this form, you can immediately see the slope and y-intercept. Also, you can quickly graph a line when the equation is written in slope-intercept form.

Graph the line given the slope and y-intercept. Try This! Graph the line given the slope and y-intercept. slope = 2, y-intercept = –3 Step 1 The y-intercept is –3, so the line contains (0, –3). Plot (0, –3). Run = 1 Step 2 Slope = Count 2 units up and 1 unit right from (0, –3) and plot another point. Rise = 2   Step 3 Draw the line through the two points.

Using Slope and a Point to Graph Graph the line with the given slope that contains the given point. slope = ; (–2, 4) (2, 7) 4 Step 1 Plot (–2, 4). • 3 (–2, 4) • Step 2 Use the slope to move from (–2, 4) to another point. Move 3 units up and 4 units right and plot another point. Step 3 Draw the line connecting the two points.

Writing Linear Equations in Slope-Intercept Form Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4). Step 1 Write the equation in point-slope form: y – y1 = m(x – x1) y – 4 = 3[x – (–1)] Step 2 Write the equation in slope-intercept form by solving for y. Rewrite subtraction of negative numbers as addition. y – 4 = 3(x + 1) y – 4 = 3x + 3 Distribute 3 on the right side. + 4 + 4 Add 4 to both sides. y = 3x + 7

Rescue Mission!

1. Each Person must plot their location using the longitude and latitude coordinates given. 2. Use the compass rose to find the direction you must wall. This directional line will help you find your rate of change (slope). Use your coordinates and slope to graph your line. 3. Using the rate of change (slope) from the compass rose and your coordinates (point), write a linear code (equation) for the path you will be walking. Will you be rescued?

4. Exchange your linear code with the other group 4. Exchange your linear code with the other group. Graph the other groups linear code (equation) on your coordinate plane. Your paths should cross, this coordinate point will be the pick up point. Write it on your paper. Will you be rescued?