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Here are some recommended readings before getting started with this lesson.
In the standard form of a line all x- and y-terms are on one side of the linear equation or function and the constant is on the other side.
Ax+By=C
In this form, A, B, and C are real numbers. It is important to know that A and B cannot both be 0. Different combinations of A, B, and C can represent the same line on a graph. It is preferred to use the smallest possible whole numbers for A, B, and C and it is also better if A is a positive number.
The given linear equation shows the relationship between the variables x and y. Determine if the equation is written in standard form.
y=0
Zero Property of Multiplication
Identity Property of Addition
LHS/3=RHS/3
x=0
Zero Property of Multiplication
Identity Property of Addition
LHS/5=RHS/5
Now it is time to plot the intercepts in a coordinate plane.
Lastly, draw a line passing through these points.
Note that general formulas for the intercepts can be derived for any linear function written in standard form Ax+By=C.
Assumption | x-intercept | y-intercept |
---|---|---|
A=0, B=0 | (AC,0) | (0,BC) |
A=0, B=0 | The line is horizontal, y=BC, so it does not cross the x-axis. | (0,BC) |
A=0, B=0 | (AC,0) | The line is vertical, x=AC, so it does not cross the y-axis. |
Tearrik is excited to buy school supplies. He plans to buy some cool pencils and notebooks.
The pencils he wants cost $2 each, and the notebooks he likes cost $5 each. He has $20 to spend. The following linear equation models this situation.y=0
Zero Property of Multiplication
Identity Property of Addition
LHS/2=RHS/2
x=0
Zero Property of Multiplication
Identity Property of Addition
LHS/5=RHS/5
The number of stationery purchased cannot be negative. In other words, stores do not sale a negative amount of products. This means that only positive values of x and y is considered in this context.
First, the x-intercept means that if Tearrik does not buy any notebooks, he can buy 10 pencils with all of his money. Whereas, the y-intercept means that if Tearrik does not buy pencils, he can buy 4 notebooks using all of his money.
LHS⋅15=RHS⋅15
Distribute 15
Commutative Property of Multiplication
ca⋅b=ca⋅b
ba=b/5a/5
ba=b/3a/3
1a=a
Multiply
LHS−y=RHS−y
Subtract terms
LHS+8=RHS+8
Commutative Property of Addition
Add terms
Rearrange equation
x=0
Zero Property of Multiplication
Subtract terms
LHS⋅(-1)=RHS⋅(-1)
Tearrik realizes at the stationery shop that the price of five pencil cases equals $10 less than the price of two school bags. The graph below shows the relationship between the price of the school bag and the price of the pencil case.
The y-intercept and the slope of the line is used to write the equation of the line in slope-intercept form. Let's first look at the y-intercept. Remember that the y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis.
The y-intercept of the line is 5. Now find the ratio of the change in y-values to the change in x-values to find the slope.
When the x-values increase by 2, y