Question

How do you graph `y= 3- 4x`?

Answer 1

See a solution process below:

Explanation:

Because this is a linear equation, first, solve for two points which solve the equation and plot these points:

First Point: For `x = 0`

`y = 3 - (4 * 0)`

`y = 3 - 0`

`y = 3` or `(0, 3)`

Second Point: For `x = 3`

`y = 3 - (4 * 3)`

`y = 3 - 12`

`y = -9` or `(3, -9)`

We can next graph the two points on the coordinate plane:

graph{(x^2+(y-3)^2-0.25)((x-3)^2+(y+9)^2-0.25)=0 [-30, 30, -15, 15]}

Now, we can draw a straight line through the two points to graph the line:

graph{(y+4x-3)(x^2+(y-3)^2-0.25)((x-3)^2+(y+9)^2-0.25)=0 [-30, 30, -15, 15]}

Answer 2

Without bothering to make ordered pairs, start at the y intercept 3, then follow the slope.
Drop down 4 and run across 1 step to another point on this line `(1,-1)`
Draw the line established by these two points.

Explanation:

The thing about the slope of a straight line is that is it always the same everywhere for that line.

In this case, the slope of `- 4` means that from any point to any other, the line has gone down 4 steps and across one step.

The reason for that is that slope equals "rise over run."
That is, it rises the number of steps in the numerator of the slope, and runs along the x axis for the number of steps in the denominator.

Example: `y = 2x + 3`
The slope of 2 (actually, `2/1`) informs you that from any point on this line, there is another point that you find by counting up 2 steps, then counting across one step. (This is "rise over run.")
Where you land is where to mark another point on the same line.

If the slope is negative, you "rise downward" -- or better to say, "drop" -- the number of points in the numerator, and then count along the x axis.
Example:
`y = - 3x + 4`
From any point on the line, to get to another point you "rise down" 3 and go across 1. That is, you drop down 3 points and go across 1,
...............................

But where is the point for you to start at?
Well, at first there is only one point that you know is on the line.
That point is `b` -- the y intercept.

So to graph the given line without bothering to make ordered pairs,
1. Put the point of your pencil on the y intercept point -- point `(0,3)`.

2) From there, count down 4 steps. You will be at `(0,-1)`

3) Then from `(0,-1)`, go across exactly one step, which will bring you to `(1,-1)`.

4) Mark that spot because it is a point on the same line.

5) You can show the line by drawing it through the two points you found: `(0,3)` and `(1,-1)`

6) You can keep on finding as many points as you want, all lying on the same line,
Just start from the most recent point `(1,-1)` and drop down 4 and run across 1. This will bring you to the point `(2,-5)`, another point on this same line.
............................

All these points are establishing a line with a downward slope of `-4` The points also show that the line has crossed the y axis up at (0,3).