writing linear equations kg math middle school
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ObjectiveThe student will be able to:
1) Graph linear equations in slope- intercept form.
2) Write equations using slope-intercept form.
3) Identify slope and y-intercept from an equation.
RememberAll we have
Learned about Lines
FORMULA FOR FINDING SLOPE
12
12
XX
YY
RUN
RISESLOPE
The formula is used when you know two points of a line.
),(),( 2211 YXBandYXAlikelookThey
EXAMPLE
Find the slope of the line between the two points (-4, 8) and (10, -4)
If it helps label the points. 1X 1Y2X 2Y
Then use the formula
12
12
XX
YY
)4()10(
)8()4(
FORMULAINTOSUBSTITUTE
7
6
14
12
)4(10
84
)4()10(
)8()4(
SimplifyThen
Graphing Linear Equations
In Slope-Intercept Form
We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line.
In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.
y 2x 1
y x 4
y 32
x 2
These equations are all in Slope-Intercept Form:
Notice that these equations are all solved for y.
Just by looking at an equation in this form, we can draw the line (no tables).
•The constant is the y-intercept.
•The coefficient is the slope.
y 2x 1
y x 4
y 3
2x 2
Constant = 1, y-intercept = 1.
Coefficient = 2, slope = 2.
Constant = -4, y-intercept = -4.
Coefficient = -1, slope = -1.
Constant = -2, y-intercept = -2.
Coefficient = 3/2, slope = 3/2.
The formula for Slope-Intercept Form is:
y mx b;• ‘b’ is the y-intercept.
• ‘m’ is the slope.
On the next three slides we will graph the three equations:
y 2x 1, y x 4, y 3
2x 2
using their y-intercepts and slopes.
y 2x 1
1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.
up 2
right 1 up 2
right 1
1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.
right 1down 1
right 1
y x 4
down 1
1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.
right 2
up 3
y 3
2x 2
right 2
up 3
Sometimes we must solve the equation for y before we can graph it.
2x y 3
2x y ( 2x) ( 2x) 3
y 2x 3
The constant, b = 3 is the y-intercept.
The coefficient, m = -2 is the slope.
1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3.
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.
right 1down 2
right 1
down 2
y 2x 3
Important!!!
This is one of the big concepts in Algebra 1. You need to thoroughly
understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept
Writing Equations
When asked to write an equation, you need to know two things – slope (m) and y-intercept (b).
There are three types of problems you will face.
Writing Equations – Type #1Write an equation in slope-intercept form of the
line that has a slope of 2 and a y-intercept of 6.
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
We have both!! Plug them into slope-intercept form
y = mx + b
y = 2x + 6
2
6
Write the equation of a line that has a y-intercept of -3 and a slope of -4.
1. y = -3x – 4
2. y = -4x – 3
3. y = -3x + 4
4. y = -4x + 3
Writing Equations – Type #2Write an equation of the line that has a slope of 3
and goes through the point (2,1).
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
We have to find the y-intercept!! Plug in the slope and ordered pair into
y = mx + b
1 = 3(2) + b
3
???
Writing Equations – Type #21 = 3(2) + b
Solve the equation for b
1 = 6 + b
-6 -6
-5 = b
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
y = 3x - 5
3
-5
Writing Equations – Type #3Write an equation of the line that goes through the
points (-2, 14) and (4, 2). To write an equation, you need two things:
slope (m) =y – intercept (b) =
We need both!! First, we have to find the slope. Plug the points into the slope formula.
FIND THE SLOPE OF the LINE using the two points. M=????
??????
Writing Equations – Type #3Write an equation of the line that goes through the
points (-2, 1) and (4, 2).
To write an equation, you need two things:
slope (m) = -2
y – intercept (b) =
It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use?
I’m using (4, 2) because both numbers are positive.
???
Writing Equations – Type #32 = (-2) (4) + b
Solve the equation for b 2 = -8 + b
+8 +8 10 =b (ADD 8 to both sides)
To write an equation, you need two things:slope (m) = -2y – intercept (b) = 10y= -2 x +10
Write an equation of the line that goes through the points (0, 1) and (1, 4).
1. y = 3x + 4
2. y = 3x + 1
3. y = -3x + 4
4. y = -3x + 1
To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b.
Find the slope and y-intercept.
1) y = 3x – 7
y = mx + b
m = 3, b = -7
Find the slope and y-intercept.
2) y = x
y = mx + b
y = x + 0
3) y = 5
y = mx + b
y = 0x + 5
2
3m =
b = 0
2
3
2
3
m = 0b = 5
-3 -3 -3
Find the slope and y-intercept.4) 5x - 3y = 6
Write it in slope-intercept form. (y = mx + b)
5x – 3y = 6
-3y = -5x + 6
y = x - 25
3m =
b = -2
5
3
Write it in slope-intercept form. (y = mx + b)
2y + 2 = 4x
2y = 4x - 2
y = 2x - 1
Find the slope and y-intercept. 5) 2y + 2 = 4x
2 2 2
m = 2b = -1
Find the slope and y-intercept of y = -2x + 4
1. m = 2; b = 4
2. m = 4; b = 2
3. m = -2; b = 4
4. m = 4; b = -2
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