SWBAT Write and graph lines in slopeintercept form

SWBAT… Write and graph lines in slope-intercept form Mon, 11/14 Agenda 1. WU (10 min) 2. Video on graphing (5 min) 3. Graphing lines (10 min) 4. Writing equations of lines in slope-intercept form Warm-Up: Solve each equation for y: 1. 2 y = 4 x + 2 2. -3 y = -9 x – 12 3. 21 x – 7 y =14 4. 2 y + 26 = -6 x

When an equation is in slope-intercept form: Now look at the equation below…… What is the slope? ______ What is the y-intercept? ______

Converting linear equations into Slope-Intercept Form 4 Warm-UP Examples

Slope intercept form is: y = mx + b Our main goal is to get the y alone on one side of the equation

Example 1 - convert into Slope-Intercept Form (divide both sides by 2 to get y alone) 2 (now simplify all fractions) 1 What is the slope? _____ What is the y-intercept? ______

Example 2 – Convert to Slope-Intercept Form -3 y = -9 x – 12 Step 1: divide both sides by -3 to get y alone Step 2: Simplify all fractions Step 3: Write your equation in y = mx + b What is the slope? ______ What is the y-intercept? ______

*** Check Your Answer *** -3 y = -9 x – 12 -3 -3 -3 (divide both sides by -3 to get y alone) (now simplify all fractions) y = 3 x + 4 Slope = 3 Intercept = 4 Wow, you’re good at this!!

Example 3: Convert to Slope-Intercept Form 21 x – 7 y =14 -7 y = -21 x + 14 (subtract both sides by 21 x) (now divide both sides by -7) (simplify all fractions) y = 3 x – 2 What is the slope? _____ What is the y-intercept? ____

Example 4: Convert to Slope-Intercept Form 2 y + 26 = -6 x Step 1: Subtract both sides by 26 Step 2: Divide both sides by 2 to get y by itself Step 3: Simplify all fractions What is the slope? ______ What is the y-intercept? ______

*** Check Your Answer *** 2 y + 26 = -6 x (subtract both sides by 26) (now divide both sides by 2 2 y = -6 x – 26 (simplify all fractions) y = -3 x – 13 You are a math wizard!

Families of Linear Graphs • http: //www. glencoe. com/sites/texas/ student/mathematics/assets/animati on/algebra 1/ALG 1 CIM 4 -3. swf

y = 2/3 x + 2 Step 2: Look at the y-intercept and plot Step 1: Solve for y y y = 2/3 x + 2 where the graph crosses the y-axis. Step 3: Use the slope (rise/run) to determine the next point and plot. Slope = 2/3 Step 4: Draw a line through both points. Be sure to extend the line and put arrows at both ends. (Use a ruler!) Step 5: Label your line x

Step 1: Solve for y Step 2: Look at the y-intercept and plot where the graph crosses the y-axis. Step 3: Use the slope (rise/run) to determine the next point and plot. Slope = 2/1 Step 4: Draw a line through both points. Be sure to extend the line and put arrows at both ends. (Use a ruler!) Step 5: Label your line y y = 2 x + 1 x

Step 1: Solve for y y Step 2: Look at the y-intercept and plot where the graph crosses the y-axis. Step 3: Use the slope (rise/run) to determine the next point and plot. Slope = -1/1 Step 4: Draw a line through both points. Be sure to extend the line and put arrows at both ends. (Use a ruler!) Step 5: Label your line y = -x – 2 x

Write the equation of the line, in slope-intercept form, that passes through (3, 5) and (5, 9) Step 1: Find the slope Step 2: Plug in either coordinate into y = mx + b and solve for b Step 3: Write the equation of the line by substituting the values you computed for m (step 1) and b (step 2) in y = mx + b m = (y 2 -y 1)/(x 2 -x 1) m = (9 -5)/(5 -3) = 4/2 = 2 (3, 5) y = mx + b 5 = 2(3) + b 5 = 6 + b -1 = b (5, 9) y = mx+b OR 9 = 2(5) + b 9 = 10 + b -1 = b y = 2 x – 1 Besides (3, 5) and (5, 9), what’s another point on this line? Hint: b=-1 (0, -1)

Ex 1: Write the equation of the line, in slope-intercept form, that passes through (3, 5) and (5, 9) Step 1: Find the slope Step 2: Plug in either coordinate into y = mx + b and solve for b Step 3: Write the equation of the line by substituting the values you computed for m (step 1) and b (step 2) in y = mx + b m = (y 2 -y 1)/(x 2 -x 1) m = (9 -5)/(5 -3) = 4/2 = 2 (3, 5) y = mx + b 5 = 2(3) + b 5 = 6 + b -1 = b (5, 9) y = mx+b OR y = 2 x – 1 9 = 2(5) + b 9 = 10 + b -1 = b

SWBAT… Write equations in slope-intercept form Tues, 1/4 Agenda 1. WU (15 min) 2. Review hw#5 (15 min) 3. Quiz (15 min) WARM-UP: Write the slope-intercept form of an equation of the line that satisfies each condition: 1. ) 2. ) 3. ) 4. ) Has slope 3 and y-intercept -5 Passes through (5, -7) and has a slope of 3 Passes through (6, -3) and (12, -3) Has an x-intercept of -2 and a y-intercept of 4 (Hint: write the two points) 2 problems