FORMS OF LINEAR EQUATIONS
FORM
Standard
SlopeIntercept
Point-Slope
Two-Point
Horizontal
Vertical
EQUATION
Ax By C
y mx b
CONDITIONS
Coefficients A and B cannot both be zero
y-intercept is (0,b), slope is m
y y1 m x x1
Line contains point (x1, y1), slope
Consecutive Integer word problems:
The first thing to accomplish when working on word problems is to Define the
Variables.
This may be as simple as stating: x is the first number and y is the second
number.
Consecutive integers are numbers such as 5 and 6
Formulas for Slope and Equations of Lines
Slope(m)
rise change in y coordinates
run change in y coordinates
Given : x1 , y1 and x2 , y2
slope (m)=
y 2 y1
x 2 x1
x1 , y1 and x2 , y2
(m)=
y 2 y1
x 2 x1
Slope Intercept Form
slope (m)=
y 2 y1
x 2 x1
Given
Given values for the domain (input), find the values of the function
(output):
f x x 2 7 x 10, find f 0
f 0 02 7 0 10 10
f x x 2 7 x 10, find f 5
f 5 5 7 5 10
2
25 35 10 0
f x x 2 7 x 10, find f 2
f 2 2 7 2 10
2
4 14 10 28
f x 4 x 3, find f 1
f 1 4 1
An airplane covered 15 miles of its route while decreasing its altitude by 24,000 ft. Find
the slope of the line of descent that was followed.
Hint: 1 mile = 5280 ft. Round to the nearest hundredth.
The horizontal distance is the miles covered during the
Section 2.3 page 96 #11
7 x 17 2 x 2 8 x 15 The first step is to combine similar terms
on the right and left sides of the equal sign.
7 x 2 x 17 2 15 8 x
9 x 17 17 8 x Now we can start "moving" terms. Start with any addition
or subtraction first. (reversi
A few thoughts about slope, points and equations of lines:
Lines consist of an infinite number of points, but we only need two points to
graph the line.
Reversing this thought, we only need two pieces of information about the line to
find the equation of
Examples of finding the missing coordinate of a point.
Given the equation 2 x 5 y 10 and x
1
1
find y , y
2
2
1
2 5 y 10 Substitute for given value for x.
2
1 5 y 10
1
-1 Subtract 1 from both sides.
5y 9
5y 9
Divide both sides by 5.
5 5
9
y
5
1 9
Poin
Five Steps for Solving Equations
Example Problem
2(w-3)-3(3w-2)=-14
Step 1: Look for Distributive Property and
Solve. Pay close attention to the signs
2(w-3)-3(3w-2)=-14
Now is:
2w-6-9w+6=-14
Step 2: Combine like terms on one or
both sides of equation.
2w
two children and describe one child as taller/shorter. Classify objects and count the number of objects in
each category. 3. Classify objects into given categories; count the numbers of objects in each category
and sort the categories by count.3 Geometry
Equation of a straight line Let L be a straight line in the plane. A first degree equation px + + qy r = 0 in
the variables x and y is satisfied by the x-coordinate and y-coordinate of any point on the line L and any
values of x and y that satisfy this eq
connected subject. Domains are larger groups of related standards. Standards from different domains
may sometimes be closely related. Number and Operations in Base Ten 3.NBT Use place value
understanding and properties of operations to perform multi-digit
^ h x y , on L. (3) Thus, y m = x c + is the equation of straight line in the Slope-Intercept form. 160 10th
Std. Mathematics Fig. 5.28 y = 4 x = 3 Fig. 5.29 L Ll Note (d) Intercepts form Suppose that the straight
line L makes non-zero intercepts a and b
perpendicular if and only if the product of their slopes is -1. That is, m1 m2 = -1. Equation of straight
lines Sl.No Straight line Equation 1. x-axis y = 0 2. y-axis x = 0 3. Parallel to x-axis y = k 4. Parallel to y-axis x
= k 5. Parallel to ax+by+c =0
intersect at a point. This point lies on both the straight lines. Hence, the point of intersection is obtained
by solving the given two equations. Example 5.26 Show that the straight lines 3 2 x y + - 12 = 0 and 6 4 x
y + + 8 0 = are parallel. Solution Sl
context. b. Combine standard function types using arithmetic operations. For example, build a function
that models the temperature of a cooling body by adding a constant function to a decaying exponential,
and relate these functions to the model. c. (+) C
Write the equations of the straight lines parallel to x- axis which are at a distance of 5 units from the xaxis. 2. Find the equations of the straight lines parallel to the coordinate axes and passing through the
point (-5,-2). 3. Find the equation of a s
Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an
equivalent fraction, and/or by using properties of operations and the relationship between addition and
subtraction. d. Solve word problems involving addit
shape" and "scale factor" developed in the middle grades. These transformations lead to the criterion for
triangle similarity that two pairs of corresponding angles are congruent. The definitions of sine, cosine,
and tangent for acute angles are founded o
two populations. Investigate chance processes and develop, use, and evaluate probability models.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly
and quantitatively. 3. Construct viable arguments and cri
quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with
mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of
structure. 8. Look for and express regularity in rep
the shape of the data distribution and the context in which the data were gathered. Common Core State
Standards for MATHEMATICS grade 7 | 46 Mathematics | Grade 7 In Grade 7, instructional time should
focus on four critical areas: (1) developing understan
of a rational number and an irrational number is irrational; and that the product of a nonzero rational
number and an irrational number is irrational. Quantities N-Q Reason quantitatively and use units to
solve problems. 1. Use units as a way to understan
(b) ^ h 2 4 a b , (c) ^ h 2 2 a b , (d) ^ h - -a b , 3 2. The point P which divides the line segment joining the
points A^ h 1 3 ,- and B^ h -3 9, internally in the ratio 1:3 is (a) ^ h 2 1, (b) ^ h 0 0, (c) , 3 5` j 2 (d) ^ h 1 2 ,3. If the line segment
analyzing and performing operations on these relationships to draw conclusions, (4) interpreting the
results of the mathematics in terms of the original situation, (5) validating the conclusions by comparing
them with the situation, and then either improv
numbers. In high school, students will be exposed to yet another extension of number, when the real
numbers are augmented by the imaginary numbers to form the complex numbers. With each extension
of number, the meanings of addition, subtraction, multiplic
or complements of other events (or, and, not). 2. Understand that two events A and B are
independent if the probability of A and B occurring together is the product of their probabilities, and use
this characterization to determine if they are independent
Four methods used to soihre quadratic equations, Mime. factoring, using the square root
tormuia, oompietlng the square, and using the quadratic tormuia. Each method oontains its own
tormuia orsoiving quadratic equations, aooor'dlirig to the oontents ofthe
Since x is on the right side, move it to the left side
Since both expressions have the same denominator, the numerators must be
equal so multiply the numerators by (-1.
It looks like this equation is Undefined.