Q&A for How to Graph Linear Equations

It means the y-intercept is 0. Let's say you have something like y = 5x + 0. The 0 would be taken out because anything plus 0 is itself.

Then the line will go from top left to bottom right. This is because the rise or run is negative.

Transfer that into a linear equation by taking 2x and reverse the -2x, which brings it to y=2x+0

Here, the slope is not x, it is the coefficient in front of the x. It doesn't seem like there is one, but remember: When a variable stands a by itself, there is an implied one in front of the variable. So the slope here is actually 1, and you can follow the standard steps for graphing a linear equation.

When the slope is a whole number, (ex. y = 2x + 3), you would put the slope over 1 to make it into a fraction (ex. y = 2/1x + 3). Then you would proceed to graph as normal.

First up, thanks for explaining your concern; we've amended the article to clarify "to the right". By way of explanation, it's as shown in the picture. If positive is one up and one right, then negative will be one down, one right. It means if the line has a slope of -1/4, every one block it goes down, it will go four blocks to the right side-by-side, not randomly. Or, you can also put it as every four blocks it goes right, it goes down one block. You can also put a negative-sloped line as one block up and four blocks left since that's what happens to negative-sloped lines. They travel from top left to bottom right. As always, a linear equation only has one solution per input.

(4,5) is correct. (-1,1) is not, because if x = -1, 2(-1) - 3 = -5.

Yes. That just means the y-intercept is on the negative (downward) portion of the y-axis.

There's always a slope. In this case, it's -1.

A horizontal line represents an equation in which there is no x, and y is equal to a constant number, such as y = 3. A vertical line represents an equation in which there is no y, and x is equal to a constant number, such as x = 5.

The line moves down as it moves to the right.

If you mean the gradient, then yes. You could also use 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡=𝑦2−𝑦1 divide by 𝑥2−𝑥1

An equation which can be represented by a straight-line graph.

(-1/3, -1/5) is a single point one-third of a unit to the left of the y-axis and one-fifth of a unit below the x-axis. A single point does not have a y-intercept (unless the x-coordinate is zero).

That is the variable which does not stand alone on one side of the equation. For example, in the equation y = 2x + 3, x is the independent variable.

As the article explains, start at the value of b (that is, where x = 0 and y = b). You can then extend the line as far as you want in each direction.

m is the coefficient of x. In this case, the coefficient is -1. A slope of -1 means that the line moves down one unit for every unit it moves to the right. Thus, the line moves down at a 45° angle from left to right. The negative value of b means that the line crosses the y-axis at -4.

Treat it as you would any y-intercept. If the y-intercept is between zero and 1 (say, .5), the line crosses the y-axis at .5. The same is true if the y-intercept is greater than 1, such as l.5 or 2.75.

That means that the graph crosses the y-axis below the x-axis.

Well, you have two options. You can convert it into slope-intercept form, or you could find two points from the equation then graph that and connect the dots. Let's say you have 5x - 5y = 25. If you want to convert it to slope-intercept form, you want to isolate y. 5x - 5y = 25 -5y = 25 - 5x y = -5 + x y = x - 5 That's slope intercept form right there. If you want to connect dots, you find two points. Let's say x = 0, the y value will be -5. If x = 1, the y value will be -4. There you have two points (0, -5) and (1, -4). So then you just connect the dots with a straight line.

The order pairs that live on its graph are (4x, x/4).

Your m is the numerical coefficient of x. In this case, the coefficient of x is 1.

The easiest thing to do here is to divide both sides of the equation by three.

That's a straight line that crosses the y-axis at +2 and moves up one unit for every unit it moves to the right (or down one unit for every unit it moves to the left).

You would move down two units for every three units moved to the right.

In terms of graphing, "the answer" is the graph of the equation. First multiply both sides of the equation by 4 to get rid of the fraction: 3x - 8y +32 = 0. Then add 8y to both sides: 3x +32 = 8y. Now divide both sides by 8: (3/8)x + 4 = y. Now assign a few values (positive and negative) to x, and calculate the corresponding y values. For convenience, choose x values that are divisible by 8 (because of the 3/8 coefficient). Now plot the graph of the equation using points corresponding to the pairs of x and y values you've developed.

If you're referring to y = mx + b, the "b" term moves the line (and the y-intercept) vertically up or down on the graph. If the "b" term is a fraction, that just means that the line moves up (or down) a fractional number of units compared to the graph of the equation without the "b" term. For example, when y = 2x + b, if "b" is ½, the line and the y-intercept move half-a-unit higher than the graph of y = 2x.

Solve for y: y = -2, which graphs as a straight, horizontal line crossing the y-axis at -2.

Solve the equation for y, then choose values for x and find the corresponding y values so that you can plot the resulting coordinates. In your example, solving for y, we find that y = (20 - x) / 4. Choose convenient values of x that result in whole numbers for y. (That's not absolutely necessary, but it makes it a little easier to plot.) Thus, if x = 0, y = 5. If x = 4, y = 4. If x= -4, y = 6. That's enough to plot the line, but you can plot as many x-y pairs as you like.

You simply choose a value -- any value -- for x, and then use the given equation to calculate the corresponding value for y. (If the equation had been given as "x=" rather than "y=", you would start by choosing values for y and calculating the corresponding values of x.).