Chapter 7 Unit Question What are the components and applications of lines on the coordinate plane?

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Presentation transcript:

Chapter 7 Unit Question What are the components and applications of lines on the coordinate plane?

Open Learning Logs Date on Left…Section 7 – 4 on right

WITHOUT ACTUALLY GRAPHING THESE LINES, please describe in words HOW you would graph each line and some characteristics of each WARM UP 7 – 4 ( 3, -8 ) Point Slope ( -3, 0 ) Point Slope ( 0, 0 ) Point Slope

Section 4 How do we find the equation for a line given its slope and point?

Homework Clicky

Point-Slope Definition Point-Slope form for the equation of a line…. y – y 1 = m(x – x 1 ) Equation of a non-vertical line with slope m and point (x 1, y 1 ) is… y - coordinate slope x - coordinate Bottom Line: Just substitute!

A line passes through (4, 2) and has a slope of ½. What’s the equation? y – y 1 = m(x – x 1 ) (x 1, y 1 ) m y – 2 = ½(x – 4)

A line passes through (-3, 6) and has a slope of -5 What’s the equation? y – y 1 = m(x – x 1 ) (x 1, y 1 ) m y – 6 = -5(x – -3) y – 6 = -5(x + 3)

Graphing… ( 2, 1 ) Point Slope Slope is a DIRECTION…it points to the next point on a line! Start at the given point… Then SAY the slope… +U 2 OVER 3 That is our direction to the next point. Up 2 Over 3

Graphing… ( -4, 3 ) Point Slope Slope is a DIRECTION…it points to the next point on a line! What is the graph of the equation y – 3 = -4(x + 4) Start at the given point… Then SAY the slope… -D 4 OVER 1 That is our direction to the next point. Down 4 Over 1 Down 4 Over 1

What is the equation of the line in point-slope form?… Find Slope first! Now go to point-slope form! y – y 1 = m(x – x 1 ) Pick a point and substitute! y – 4 = (x – 1) (1, 4) (-2, -3)

The table shows the descent of a hot air balloon. timealtitude xy What is the equation of the line that represents the descent? y – y 1 = m(x – x 1 ) y – 640 = – 2.5 (x – 10) Fantastic! Now solve for y! y – 640 = – 2.5x y = – 2.5x This form is called the Slope-Intercept form We’ll be talking more about this tomorrow!

Homework Do HoffmaSheet 7 – 4