The document discusses various formulas used to represent lines in the coordinate plane, including: - Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. - Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope. - Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0. It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between

1. 18
Today:

2. 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?

3. Answers:
2. Domain: {-4, -2, 3, 4} Range: {-2, 2, 1}
Not a
Function
Function
Not a
Function
4b.
0
1
7
-6
2
-4
4
3. 4a.
1. f(x) = -2x + 3 ; {-5, -2, 6}; The range values are: {-13, 7, -9};

4. Describe the Slope

5. Describe the Slope

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

7. 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.

8. 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
10
20
30
40
50
60
70
80
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:

9. Graph the following equation with a minimum of
three points: y = -3x - 5
Standard Form
3x +y = - 5
What is the slope? (-
𝟓
𝟑
,0) (0,-5) m = -3
Thankfully, there's an easier way...

10. 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

11. 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 = -24 2. 5x - 3y = - 4
Practice: The Slope-Intercept Form
Write the equation for the graph

12. When to use the slope-intercept form of a line:
1. Find the equation of the line
that has a slope of
𝟏
𝟒
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 =
𝟏
𝟒
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

13. 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 = -
𝟐
𝟑
x - 2

14. Practice: Slope-Intercept Formula
Then use the slope to plot other points.
1. Given a y intercept of 2, and a slope of
𝟏
𝟒
,
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 =
𝟏
𝟒
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:

15. 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:

16. The only information you have is the slope
𝟑
𝟒
, 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 =
𝟑
𝟒
(x – 1); =
What do you notice about the point-slope formula?

17. 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 =
𝟑
𝟒
x +
𝟓
𝟒

18. 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:

19. 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

20. Point-Slope: Two points
STEP 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...

21. Formulas for the Coordinate Plane