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Here are a few 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.
Consider the given linear equation that shows the relationship between the variables $x$ and $y.$ Determine whether the equation is written in standard form or not.
$y=0$
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. 
$yintercept:$ $(0,6)$
$y=0$
Zero Property of Multiplication
Identity Property of Addition
$LHS/3=RHS/3$
$x=0$
Zero Property of Multiplication
Identity Property of Addition
$LHS/4=RHS/4$
Since the number of kilograms of fruit purchased cannot be negative, only positive values of $x$ and $y$ make sense in this context.
Job  Amount Paid Per Hour $($)$  Amount LaShay Makes $($)$ 

I  $7$  $7x$ 
II  $10$  $10y$ 
$7x+10y=350$  

Operation  $x$intercept  $y$intercept 
Substitution  $7x+10(0)=350$  $7(0)+10y=350$ 
Calculation  $x=50$  $y=35$ 
Point  $(50,0)$  $(0,35)$ 
Now, plot the intercepts on a coordinate plane and connect them with a line segment. Since the number of hours worked cannot be negative, only positive values of $x$ and $y$ make sense.
$LHS⋅15=RHS⋅15$
Distribute $15$
Commutative Property of Multiplication
$ca ⋅b=ca⋅b $
$ba =b/5a/5 $
$ba =b/3a/3 $
$1a =a$
Multiply
Jordan wants to buy some songs and movies online to enjoy after school. She can buy songs for $$0.75$ each and movies for $$5$ each. The graph represents the relationship between the number of songs purchased $x$ and the number of movies purchased $y.$
Write an equation in standard form that describes the relationship between $x$ and $y.$ Give the answer such that $A,$ $B,$ and $C$ are the smallest possible integers and $A$ is positive.Start by writing the equation of the line in pointslope form. Then, convert it into the standard form.
From the given graph, the $x$ and $y$intercepts can be identified.
The intercepts are $(60,0)$ and $(9,0).$ When two points on a line are known, the pointslope form can be used to write the equation of the line. Recall that an equation in pointslope form follows a specific format.Substitute $(60,0)$ & $(0,9)$
Subtract terms
$ba =b/3a/3 $
Put minus sign in front of fraction
$x=0$, $y=9$
Zero Property of Multiplication
Multiply
Identity Property of Addition
Rearrange equation
The equation found by Dominika is written in pointslope form and the other equation is written in slopeintercept form.
PointSlope Form  SlopeIntercept Form 

$y−y_{1}=m(x−x_{1})$  $y=mx+b$ 
$Dominika’s Equationy−43 =43 (x−12) $

$Ali’s Equationy=43 x+(433 ) $

However, Dominika's calculations are not entirely correct. Until the last step everything is correct. However, she made a mistake when factoring out $43 .$
The given equation can be written correctly in pointslope form as follows.Rewrite $36$ as $3⋅12$
$ca⋅b =ca ⋅b$
Factor out $43 $
For each line there is exactly one equation in standard form that meets these properties. However, infinitely many equivalent linear equations in standard form can be obtained by using the Multiplication Property of Equality. Linear equations are equivalent if they describe the same line.