Topic 2 Linear Equations Part 1

Presentation

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Mathematics

•

9th Grade

•

Medium

•

CCSS

HSA.CED.A.2, 8.EE.B.5, 8.EE.B.6

Standards-aligned

Tara Palmer

Used 5+ times

FREE Resource

12 Slides • 29 Questions

Topic 2 Linear Equations

Mrs. Palmer

Slope-Intercept Form

Slope Intercept Form

Shows you 2 pieces of information

1. Slope: also known as 'm'

\frac{rise}{run}\ \ \ \ \ \ \frac{\Delta y}{\Delta x}\ \ \ \ \ \ \frac{y_2-y_1}{x_2-x_1}

2. y-intercept: also known as 'b'
(this is the constant in every

y=mx+b

Multiple Choice

What is the slope of the following equation?

y=-\frac{1}{5}x+10

-1/5

1/5

-5

Multiple Choice

What is the y-intercept of the following equation?

y=-\frac{1}{5}x+10

$-\frac{1}{5}$

-10

$\frac{1}{10}$

Multiple Choice

What is the slope of the following equation?

y=4x-3

-4

$\frac{1}{4}$

$-\frac{1}{4}$

-3

Multiple Choice

What is the y-intercept of the following equation?

y=4x-3

-4

-3

$-\frac{1}{3}$

$\frac{1}{4}$

Multiple Choice

Which graphs has a slope of 2 and a y-intercept of 3?

Red

Blue

Green

Purple

Point-Slope Form

Gives you 2 pieces of information...
1) An ordered pair

$\left(x_1\ ,\ y_1\right)$

2) Slope

Poll

True or False:
The ordered pair in this equation

$y-3=2\left(x-4\right)$ is (4,3)

True

False

Point-Slope Form

$y-y_1=m\left(x-x_1\right)$

What is the ordered pair and the slope for the following equation? $y-5=-2\left(x-3\right)$

$y-y_1=m\left(x-x_1\right)$

$y-5=-2\left(x-3\right)$

y-5\ =\ -2\left(x-3\right)

$m\ =\ -2\ or\ -\frac{2}{1}$

\left(x_1\ ,\ y_1\right)=\left(3,5\right)

Multiple Select

What is the slope and ordered pair of the following point-slope equation?

$y+2=3\left(x-4\right)$

$m\ =3$

$m=\frac{1}{3}$

$\left(-4,2\right)$

$\left(4,\ -2\right)$

Multiple Select

What is the slope and ordered pair of the following Point-Slope Equation?

y+3\ =\ \frac{1}{2}\left(x+4\right)

$m=\frac{1}{2}$

$m=-\frac{1}{2}$

$\left(4,3\right)$

$\left(-4,\ -3\right)$

Standard Form

Ax+By=C

helps you find the x-intercept and y-intercept quickly!

Standard Form:

$2x+4y=16$
$A=2,B=4,C=16$

x-Intercept (when y=0)

$2x+4y=16$
$2x=16$ (divide both sides by 2)
$x=8$
$\left(8,0\right)$

y-Intercept (when x = 0)

$2x+4y=16$
$4y=16$ (divide both sides by 4)
$x=4$
$\left(0,\ 4\right)$

Graph the two ordered pairs and connect with a straight line. $(8,0)\ and\ (0,4)$

Multiple Choice

Which Graph Represents this Standard Form Equation?

$4x+3y=12$

Multiple Choice

Which Graph Represents this Standard Form Equation?

$2x+8y=8$

Multiple Choice

Find the slope from the table.

-4

-2

Multiple Choice

What is the equation of the line in the graph?

y = 3

x = 3

x = 0

Multiple Choice

Give the equation for the graph

y = 5x - 3

y = 4x + 2

y =-2x + 5

y = - 2x + 4

Multiple Choice

What letter represents the slope of a line in the equation y = mx + b?

Multiple Choice

What is the equation for the line that passes through the points (4,2) and (0,6)?

y = x + 6

y = -2x + 2

y = -x - 6

y = -x + 6

Multiple Choice

What is the slope of the line passing through the points (3,5) and (-1,7)?

-1/2

-1

-2

1/2

Multiple Choice

What does the "b" stand for in y=mx+b?

slope

x-intercept

y-intercept

Multiple Choice

Find the x and y intercepts
4x - 5y = 40

x intercept is 10
y intercept is 8

x intercept is 10
y intercept is 20

x intercept is 8
y intercept is 10

x intercept is 10
y intercept is -8

Multiple Choice

Give the x-intercept
3x + 8y = 24

(8, 0)

(0, 8)

(3, 0)

(0, 3)

Multiple Choice

Name the x- and y-intercepts for the equation:
2x + y = 6

(0, 3) and (6, 0)

(0, -3) and (-6, 0)

(3, 0) and (0, 6)

(-3, 0) and (0, -6)

Multiple Choice

What is the formula for Point-Slope Form?

y - y₁ = m(x - x₁)

y = mx + b

y + y₁ = m(x + x₁)

y = mx - b

Multiple Choice

What is the formula to Slope-Intercept Form?

y = mx + b

y - y₁ = m(x - x₁)

x = my + b

funky chickens

Multiple Choice

For the equation
y - 4 = -1/3(x - 7),
what are the coordinates for the point?

(4, 7)

(-7, - 4)

(7, 4)

(-4, -7)

Multiple Choice

Which of these represents slope-intercept form of a linear equation?

y - y₁ = m(x-x₁)

Ax + By = C

y = mx + b

y=kx

Multiple Choice

Which of these represents point-slope form of a linear equation?

y - y₁ = m(x - x₁)

Ax + By = C

y = mx + b

y=kx

Multiple Choice

Write an equation in point slope form of equation of line

point (7,10) and has a slope of -2?

y-10 = -2(x+7)

y-10 = -2(x-7)

y+10 = -2(x+10)

y -10 = -2x+2

Multiple Choice

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

Parallel

Perpendicular

Neither

Multiple Choice

The slopes of parallel lines are...

the same

opposite

always different

Multiple Choice

Find the slope

-5/3

-3/5

5/3

3/5

Topic 2 Linear Equations

Mrs. Palmer

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