Warm up 8/24 Solve each equation for y. 1. 7x + 2y = 6 2. 3. If 3x = 4y + 12, find y when x = 0. 4. If a line passes through (–5, 0) and (0, 2), then it passes through all but which quadrant. y = –2x – 8 y = –3 IV

Agenda: Warmup Go over hw p. 94 & 100 Note 2.3 & 2.4 notes Be seated before the bell rings DESK Warm-up (in your notes) Agenda: Warmup Go over hw p. 94 & 100 Note 2.3 & 2.4 notes homework Quiz – Tuesday 8/12 Tomorrow

Don’t forget test retakes

Notebook 7) 2.3 & 2.4 Table of content 2.3 Graph linear function/ 1 Table of content 2.3 Graph linear function/ 2.4 Writing linear functions Page 1) 1-1 Sets of Numbers /1.2 Properties of Numbers 1 2) 1-3 Square Roots 3) 1-4 Simplify Algebra Expression 4) 1.6 Relations/1.7 functions 5) 1.9 Parent Functions 6) 2.1 Linear Equations/ 2.2 Proportions 7) 2.3 & 2.4

2.3 Graph & (2.4) write linear functions Learning targets 2.3: I can graph linear equations using slope and a point 2.3: I can graph linear equations using intercepts 2.3: I can graph linear equations in slope-intercept form 2.4: I can write the equation of a line in slope intercept form 2.4: I can write the equation of parallel and perpendicular lines in slope-intercept form

Write down as many word as you can about linear functions. 2.3 Graph & (2.4) write linear functions How much do you know Write down as many word as you can about linear functions. ______________

2.3 Graph & (2.4) write linear functions Functions 𝟏, 𝟐, and 𝟑 have the tables shown below. Examine each of them, make a conjecture about which will be linear, and justify your claim.

2.3 Graph & (2.4) write linear functions +2 –1 +2 –1 +2 –1 A linear function has a constant rate of change x –2 2 4 f(x) 1 –1 constant rate of change = Slope (m)

Graphing Linear Functions 3 ways to graph: With y-intercept and slope With a point and a slope With x and y-intercepts

1st way Slope-Intercept Form: y=mx+b Example: y=-3/4x+3

2nd Way Point & Slope: has a slope m and passes through the point (x,y) Example: slope of 3/2 and goes through (2,2)

3rd way Intercepts: Find the intercepts and graph. Example: y=-x+2 y-intercept: y=-(0)+2 y=2 x-intercept: (0)=-x+2 2=x Intercepts: Find the intercepts and graph. To find y-intercept: plug in 0 for x To find x-intercept: plug in 0 for y

Vertical Lines Horizontal Lines .

2.4 Writing equations Use: y=mx+b or y-y1= m(x-x1)b Slope (m) y-intercept Point (x1, y1)b

Writing equations

Find equation of line given two points (–1, 1) and (2, –5).

You try! Find equation of line given two points (–2, 2) and (2, –4) in point slope form.

Parallel and Perpendicular Lines

OUT S l o p e the same Parallel Lines have ___ ___ ____ ___ ___ ____ ___ ___ ____ ______ S l o p e the same

OUT S l o p e Perpendicular Lines have Negative Reciprocals ___ ___ ___ ___ ___ ___ ___ ___ ____ ___ _____ S l o p e Negative Reciprocals

Parallel and perpendicular lines Same slope Opposite reciprocal

Parallel Line: Have the same slopes Perpendicular Line: Perpendicular Line: Have negative reciprocal slopes negative reciprocal

Parallel Lines Rewrite in y = mx+ b -2x -2x 4y = -2x +9 4 4 4 Are the two lines Parallel or Perpendicular? y= m x + b slope Rewrite in y = mx+ b -2x -2x 4y = -2x +9 4 4 4 Parallel Lines

Neither Lines Rewrite in y = mx+ b -4 -4 X - 4 = -5y -5 -5 -5 Are the two lines Parallel or Perpendicular? y= m x + b slope Rewrite in y = mx+ b -4 -4 X - 4 = -5y -5 -5 -5 Neither Lines

Perpendicular Lines Are the two lines Parallel or Perpendicular? y= m x + b slope Perpendicular Lines

Write the equation of Parallel line in the form y= m x + b Example 1: Write the equation of a line that is parallel to y = -4x + 3 that contains P(1,-2). -4 P(1,-2) Step 1: Step 1: Find slope and a point Step 2: Step 2: Substitute slope and the point into the point-slope form equation. -2 -4 1 Step 3: Rewrite in y = mx + b form. Step 3:

Perpendicular Lines in the form y= m x + b Example 1: Write the equation of a line that is perpendicular to to y = -3x -5 that contains P(-3,7). 3 P(-3,7) Steps1: Find slope and a point Steps1: 1 m= Steps2: Steps2: Substitute slope and the point into the point-slope form equation. 7 1/3 -3 Steps3: Rewrite in y = mx + b form. Steps3:

Write the equation of the line in slope-intercept form. You try! Example Write the equation of the line in slope-intercept form. parallel to y = 5x – 3 and through (1, 4) m = 5 Parallel lines have equal slopes. y – 4 = 5(x – 1) Use y – y1 = m(x – x1) with (x1, y1) = (5, 2). y – 4 = 5x – 5 Distributive property. y = 5x – 1 Simplify.

Write the equation of the line in slope-intercept form. You try Write the equation of the line in slope-intercept form. perpendicular to and through (0, –2) The slope of the given line is , so the slope of the perpendicular, line is the opposite reciprocal . Use y – y1 = m(x – x1). y + 2 is equivalent to y – (–2). Distributive property. Simplify.

Summarize: In 10 words are less summarize the what you learned. Shared with your group which concept today will most likely appear on the test.