SOLUTION: Can you explain how to graph linear equations, for ex. y = 2x, y = 5-x and 4x + 6y = 8

Question 166674This question is from textbook
: Can you explain how to graph linear equations, for ex. y = 2x, y = 5-x and 4x + 6y = 8 This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Let's graph

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like

Since this tells us that the y-intercept is

.Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

Now since the slope is comprised of the "rise" over the "run" this means

Also, because the slope is , this means:

which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1

So starting at

, go up 2 units

and to the right 1 unit to get to the next point

Now draw a line through these points to graph

So this is the graph of through the points

and

# 2

Let's graph

First rearrange the terms to get

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since this tells us that the y-intercept is

.Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point

Now since the slope is comprised of the "rise" over the "run" this means

Also, because the slope is , this means:

which shows us that the rise is -1 and the run is 1. This means that to go from point to point, we can go down 1 and over 1

So starting at

, go down 1 unit

and to the right 1 unit to get to the next point

Now draw a line through these points to graph

So this is the graph of through the points

and

# 3

In order to graph ANY linear equation, you MUST solve for "y" first.

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

Now let's graph

In order to graph this equation, we only need two points to create a straight line

----------------Let's find the first point----------------------

Start with the given equation

Plug in

Multiply and to get

Add the fractions

Reduce

So when , we have the value . This means we have the first point

----------------Let's find the first point----------------------

Start with the given equation

Plug in

Multiply and to get

Add

Reduce

So when , we have the value . This means we have the second point

------------------------------------------------------------------------------------------------

So we have the two points:

and

Now plot these two points on a coordinate system

Now draw a straight line through the two points. This line is the graph of

Graph of through the two points

and

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