Chapter 4 4-7 Point slope Form. Objectives O Graph a line and write a linear equation using...
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Transcript of Chapter 4 4-7 Point slope Form. Objectives O Graph a line and write a linear equation using...
Chapter 4 4-7 Point slope Form
ObjectivesO Graph a line and write a linear
equation using point-slope form.
O Write a linear equation given two points.
Slope formulaO If you know the slope and any point
on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1) . Let (x, y) be any other point on the line.
Slope formula
Point-slope formula
Example#1O Write an equation in point slope
form for the line with the given slope that contains the given point.
Example #2O Write an equation in point slope
form for the line with the given slope that contains the given point.
O slope = 1; (–1, –4)
Example#3O Write an equation in point slope
form for the line with the given slope that contains the given point.
Student guided practice
O Do problems 1-3 in your book page 279.
Point-slope formO In previous lessons, you graphed a
line given its equation in slope-intercept form. You can also graph a line when given its equation in point-slope form. Start by using the equation to identify a point on the line. Then use the slope of the line to identify a second point.
Example#4O Graph the line described by the
equation.O y – 1 = 2(x – 3)O Solution:O y – 1 = 2(x – 3) is in the form O y – y1= m(x – x1).
O The line contains the point (3, 1).
SolutionExample#4
O Step 1 Plot (3, 1).O Step 2 Count 2 units up and 1 unit
right and plot another point.O Step 3 Draw the line connecting the
two points.
Example#5O Graph the line described by the
equation.
Solution to Example#5
O Step 1 Plot (–2, 4).O Step 2 Count 3 units up and 4 units
right and plot another point.O Step 3 Draw the line connecting the
two points.
Example#6O Graph the line described by the
equation.O y + 3 = 0(x – 4)
Solution to example#6O Step 1 Plot (4, –3).O Step 2 There slope is 0. Every value
of x will be at y = –3.O Step 3 Draw the line connecting the
points.
Student guided practice
O Do problems 4-6 in your book page 279
Exaxmple#7O Write the equation that
describes each line in slope-intercept form.
O Slope = 3, (–1, 4) is on the line.O Solution:O Step 1 Write the equation in point-
slope form:O y – y1 = m(x – x1)
O y – 4 = 3[x – (–1)]
Solution to Example#7O Step 2 Write the equation in slope-
intercept form by solving for y.O y – 4 = 3(x + 1).O y – 4 = 3x + 3Distribute 3 on the right
side.+ 4 + 4 Add 4 to both sides.
y = 3x + 7
Example#8O Write the equation that
describes the line in slope-intercept form.
O (2, –3) and (4, 1)
Example#9O Write the equation that
describes the line in slope-intercept form.
Student guided practice
O Do problems 7-9 in your book page 279
Finding intercepts O The points (1, –2) and (3, 10) are
on a line . Find the intercepts.
Example#10O The points (2, 15) and (–4, –3) are
on a line. Find the intercepts.
Student guided practice
O Do problems 13 and 14 in your book page 279.
Problem solving application
O 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.
solution
Problem solving application
O What if…? 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.
solution
Homework O Do evens problems from 23-33 pg.
280
ClosureO Today we learned how to write
equations in slope intercept form.O Next class we are going to have a
discovery activity to find the line of best fit.
Have a great day