Linear Equation Word Problems Standard Form

​Linear Equations in Standard Form

Standard Form

Standard form of a linear equation is of the form:

​

Ax + By = C​

​

Where A, B and C are integers.​

Integers are positive or negative whole numbers.

Multiple Select

Which of the following are examples of linear equations in standard form?

• $$2x+3y=6$$  

• $$y=3x-1$$  

• $$\frac{1}{3}x-\frac{4}{5}y=2$$  

• $$3x-4y=12$$  

Recall that x-intercepts have a y-coordinate of 0. They will have the form (#, 0).

and y-intercepts have an x-coordinate of ​0, they will have the form (0,#).

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Intercepts

Multiple Select

Which of the following are examples of x-intercepts?

• (0, 8)

• (-3, 0)

• (0, 0)

• (2, 2)

Multiple Select

Which of the following are examples of y-intercepts?

• (0, 0)

• (0, 2)

• (4, 0)

• (4, 4)

We set y=0 and we are left with

2x=12 and we find that x=6.

This means the x-intercept is (6,0).

To find the x-intercept:

​We set x=0 and we are left with

3y=12 and we find that y=4.

This means the y-intercept is (0,4).​

To find the y-intercept:​

Consider the equation 2x+3y=12

In short, to find y-intercepts, set x=0 and solve for y and to find x-intercepts, set y=0 and solve for x.​

Plot your intercepts and connect them with a line. Our intercepts were:

(0, 4) & (6, 0)​

​

​

Now we can graph the line 2x+3y=12 using intercepts.​

​

Multiple Choice

What is the x-intercept of the line $$5x-2y=10$$  ?

• (2, 0)

• (0, 2)

• (-5, 0)

• (0, -5)

Multiple Choice

What is the y-intercept of the line $$5x-2y=10$$  

• (-5, 0)

• (2, 0)

• (0, -5)

• (0, 2)

Draw

Sketch the line given by the equation $$5x-2y=10$$  

Writing an Equation in Standard Form

Sometimes, you may be given a table or graph and be asked to write an equation in standard form.

In these situations, we will write the equation in slope-intercept form first and then convert to standard form.

Let's practice converting from slope-intercept form to standard form first.​

Recall slope-intercept form is y=mx+b.

1. Move all variables to one side of the equation.

2. Multiply all terms by the denominator to make A, B and C integers.

Converting from y=mx+b to Ax+By=C

Multiple Choice

What is $$y=-2x-\frac{2}{7}$$   in standard form?

• $$2x+y=-\frac{2}{7}$$  

• $$2x+y=-2$$  

• $$7x+7y=-2$$  

• $$14x+7y=-2$$  

1. Isolate the y term on one side of the equation by subtracting x from both sides.

2. Divide every term by -4 to get y by itself. ​

Finding the slope of a line in standard form:

3/4 turns positive because we are dividing -3 by -4. The slope of the line is 3/4 and the y-intercept is -6.

It will be easiest to convert to slope-intercept form to find slope:

Multiple Choice

Convert $$2x+8y=24$$  to slope intercept form.

• $$y=-4x+3$$  

• $$y=-\frac{1}{4}x+3$$  

• $$8y=-2x+24$$

• $$y=4x-3$$  

After this lesson, you should have a basic understanding of...

1. ​Finding x and y intercepts from standard form.

2. Graphing a line from standard form using x and y intercepts​.

3. Converting from slope intercept form to standard form.

4. Converting form standard form to slope-intercept form.

Let me know how you feel on the next slide!

Poll

I feel like I have a good understanding of: (select as many as you want)

• Finding intercepts

• Graphing using intercepts

• Converting from slope intercept form to standard form

• Converting from standard form to slope intercept form

Poll

I feel like I need more help understanding: (select as many as you want)

• Finding intercepts

• Graphing using intercepts

• Converting from slope intercept form to standard form

• Converting from standard form to slope intercept form