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Review for Test (Friday) Review Standard Form/Slope

Slope-Intercept Form Point-Slope Form

CW 3.6 Distributed

Today:

Test Review

2. Identify the domain and range of the following relations:

{(-4,-1) ; (-2, 2) ; (3, 1) ; (4, 2)}

4. Graph the following relations and use the vertical line test to see if the relation is a function. Connect the pairs in the given order.

a. {(-3,-3) ; (0, 6) ; (3, -3)}b. {(0,6) ; (3, 3) ; (0, 0)}

3. Use mapping to see if the following relations are functions: {(0,-6) ; (1, 2) ; (7, -4) ; (1, 4)}

1. Find the range values of the function for the given domain.

f(x) = -2x + 3 ; {-5, -2, 6}

Is the relation a function?

Answers:

2. Domain: {-4, -2, 3, 4} Range: {-2, 2, 1}

Not a Functio

n

Function

Not a Functio

n

4b.

017

-62-44

3. 4a.

1. f(x) = -2x + 3 ; {-5, -2, 6}; The range values are: {-13, 7, -9};

Describe the Slope

Describe the Slope

A point on the graph is located at (-2,-3). The slope of the line is - . Find the two points nearest the given point.

Slope:

Your Journey begins here,

at the 12,000 ft. level.

Soon, you begin your descent down the mountain. After 5 hours, you are here.

What is your rate of change in elevation? (The slope of your

descent.)The rate should be in ft./hr.

Slope: Rate of Change

1700ft./hr.

The table shows how much money Susan earned as a house painter for one afternoon. Use the data to make a graph. Find the slope of the line and explain what it shows.

x

y

642 8 10 12 140

1020304050607080

The slope of the line is 7. This means Susan earned $7 for each

hour worked.What is the Y-intercept? Why?

Rate of Change:

Graph the following equation with a minimum of three points: y = -3x - 5

Standard Form

3x +y = - 5What is the

slope? (- ,0) (0,-5)

m = -3

Thankfully, there's an easier way...

A linear equation written in the form y = mx + b is in slope-intercept form.

To graph an equation in slope-intercept form:1. Write the equation in the form y = mx + b.

Identify m and b.

The slope is m and the y-intercept is (0, b).

2. Plot the y-intercept (0, b).3. Starting at the y-intercept, find another point on the line using the slope.4. Draw the line through (0, b) and the point located using the slope.

The Slope Intercept Form of a Line:

Slope-intercept form: *Your best friend in the coordinate world

Each of the following equations is in standard form. Solve for y in terms of x and use the resulting

equation to determine the slope of the graph of the equation.1. 4x - 6y = -

242. 5x - 3y = - 4

Practice: The Slope-Intercept Form

Write the equation for the graph

When to use the slope-intercept form of a line:

1. Find the equation of the line that has a slope of and a y-intercept of 2.

1. When you're given the slope and the intercept and need to write the equation/draw the graph.

y = mx + b y = x + 2

1a. When drawing a graph using the slope-intercept form, always start with the intercept, then use the slope (in both directions) to plot and draw the line.Other, more often used situations for the slope-intercept

When to use the slope-intercept form of a line:

2. When you're graphing the line of an equation, no matter what form the equation is in.y + 2 = 3x

becomes...y = 3x - 2

2a. Graph this equation using the intercept and one point above and one point below the intercept. 3. When writing the

equation of a line that crosses the y axis. (And almost all lines cross at some point)3a. Write the equation of the line shown.y = - x -

2

Practice: Slope-Intercept Formula

Then use the slope to plot other points.

1. Given a y intercept of 2, and a slope of , a) Graph the line and write the equation in both the b) slope-intercept form and c) standard form with integers only.The easiest place to start is probably the slope-intercept form, which is...b) Slope-intercept form: y = x + 2 Next we'll graph it. What's the first point plotted on the graph?

What are the coordinates of

this point?

(4,3)

a) Last, because the standard form is written in integers only, we will keep with tradition and do that. How?

The resulting equation is.. Standard form, Integers only: 4y = x + 8; -x + 4y =

8; x - 4y = -8 The coodinates of x intercept are:

1. What is the slope of the line?2. Write the equation of the line in slope intercept

form.3. What is the value of y when x is -130?

Slope-Intercept:

The only information you have is the slope , and a point on the line, but that point is not the y-intercept, say, point (1,2).

Introducing the last of our formulas, the point-slope:

What if:

Point-slope form: y – y1 = m(x – x1), where:• y and x are variables, and remain y and x

• y1 and x1 are the coordinates of the point that is known.Graph the line and write the equation

of the line given the information above.y – 2 = (x – 1); =

What do you notice about the point-slope formula?

The known point is (1, 2). Name the next point above

and below this point.

When simplified, the point-slope formula ends up as the slope-intercept form of the line. Point-slope is the starting formula, slope-intercept is the ending form of the line.

always

y = x +

Write the standard form for the equation of the line through the point (-2, 5) with a slope of 3. Use the point-slope form, y – y1 = m(x – x1), with m =

3 and (x1, y1) = (-2, 5).

y – y1 = m(x – x1)Point-slope form

y – y1 = 3(x – x1)

Let m = 3.

y – 5 = 3(x – (-2)) Let (x1, y1) = (-2, 5).

y – 5 = 3(x + 2) Simplify.

y = 3x + 11 Slope-intercept form

3x – y = - 11 Standard Form

Point-Slope:

SOLUTION

y – y1 = m(x – x1)

Calculate the slope.STEP 1

–3m = 1 – (–2)1 – 2 = 3

–1 =

Write an equation in point-slope form. Use (1, 1).

Write point-slope form.y – 1 = –3(x – 1) Substitute 1 for y1, 3

for m and 1 for x1.

Write an equation in standard form of the line shown.

STEP 2

Point-Slope: Two points

Point-Slope: Two pointsSTEP 3 y – 1 = –3(x –

1) =When simplified, the point-slope formula ends up as the slope-intercept form of the line. Point-slope is the starting formula, slope-intercept is the ending form of the line.

always

y = –3x + 4

STEP 4

Write an equation in standard form of the line shown.The original task:

Change the slope intercept form to the standard form of the line

3x + y = 4

Although the graph doesn't show the y intercept, we can use point (1, 1) and the slope, or the standard form of the line, to know that the y intercept occurs at...

Formulas for the Coordinate Plane