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### Course: 8th grade (Illustrative Mathematics) > Unit 3

Lesson 8: Extra practice: Slope# Graphing slope-intercept form

Learn how to graph lines whose equations are given in the slope-intercept form y=mx+b.

If you haven't read it yet, you might want to start with our introduction to slope-intercept form.

## Graphing lines with integer slopes

Let's graph $y=2x+3$ .

Recall that in the general slope-intercept equation $y={m}x+{b}$ , the slope is given by ${m}$ and the $y$ -intercept is given by ${b}$ .
Therefore, the slope of $y={2}x+{3}$ is ${2}$ and the $y$ -intercept is $(0,{3})$ .

In order to graph a line, we need two points on that line. We already know that $(0,{3})$ is on the line.

Additionally, because the slope of the line is ${2}$ , we know that the point $(0{+1},{3}{+2})=(1,5)$ is also on the line.

## Check your understanding

## Graphing lines with fractional slope

Let's graph $y={{\displaystyle \frac{2}{3}}}x{+1}$ .

As before, we can tell that the line passes through the $y$ -intercept $(0,{1})$ , and through an additional point $(0{+1},{1}{+{\displaystyle \frac{2}{3}}})=(1,1{\displaystyle \frac{2}{3}})$ .

While it is true that the point $(1,1{\displaystyle \frac{2}{3}})$ is on the line, we can't plot points with fractional coordinates as precisely as we draw points with integer coordinates.

We need a way to find another point on the line whose coordinates are integers. To do that, we use the fact that in a slope of ${{\displaystyle \frac{2}{3}}}$ , increasing $x$ by ${3}$ units will cause $y$ to increase by ${2}$ units.

This gives us the additional point $(0{+3},{1}{+2})=(3,3)$ .

## Check your understanding

## Want to join the conversation?

- How come if the negative sign is next to the fraction it causes the rise to be negative but not the run(47 votes)
- Think about the fraction as division... How do you get a negative number when dividing:

a negative divided by a positive = a negative

a positive divided by a negative = a negative

As you can see, only one of the 2 numbers can be negative. Thus, for a slope like -4/5, you can apply the negative sign to the numerator which would tell you to go down 4 units, then right 5 units. Or, you can apply the negative to the denominator which would make you go up 4 units and left 5 units.

If you make both numbers negative, then you are doing: negative divided by negative = positive. And, you would have a positive slope.

Hope this helps.(101 votes)

- i don't really get it why in the last exercise the slope is -3/2 you ad plus 2 for the change in x but minus 3 for the change in y.(35 votes)
- When you have a negative slope, like -3/2 then one of the numbers must be negative (remember, negative divided by positive = negative; and positive divided by negative = negative).

So, when you interpret the slope of -3.2...

1) You can do -3 for change in Y (move down 3 units) and +2 for X (move right 2 units). OR... 2) You can do +3 for change in Y (up 3 units) and -2 for X (move left 2 units).

Hope this helps.(79 votes)

- im having some trouble... anybody have some helpful tips hehehe(16 votes)
- place you first point on the y axis +/-. Then turn the slope into a fraction.

Slope: The positive or negative sign determine if the line goes up or down from the y intercept. Based on that, going left to right, if it is a negative travel down the numerator, travel right the denominator.

Y=27/3x+1 Place first point on y axis at positive 1. Then travel up 27, then go right 3. Simplified, you would go up 9, and right 1.(3 votes)

- I don't have a clue on how to do this(15 votes)
- If you have an equation in slope-intercept form, you know both a point (the y intercept) and the slope, so it should be relatively easy to graph especially with a little practice. So if you have y=3x-4, the slope is 3=3/1, the y intercept is (0,-4). We can plot the point by starting at the origin and counting down 4 to get to (0,-4) and put a dot at this point. With a slope of rise (up) 3 over run (right) 1, you get to (0+1,-4+3) which is (1,-1), and a second time (1+1,-1+3) which is (2,2) and you have three points to draw a line through. One more example, if you have y=-3/4x + 2, you have a point (0,2) and a slope of -3/4 (rise down 3 right 4). This gives a second point of (0+4,2-3) or (4,-1) and (4+4,-1-3) or (8,-4) to draw a line. So start with the y intercept, and count the slope from that point.(14 votes)

- How do I graph a line if the slope isn't provided? Here is what I mean:

y=-x+6

How do I graph it if I do not know the slope? Thanks!(14 votes)- When a variable doesn't have a variable, it's safe to assume the variable is 1. So, -x would be -1x or -1/1x.

Hope that makes sense!(11 votes)

- Not to be that person but like When am I reallyyyyyyyyyyyy going to use this in everyday life?(11 votes)
- my teacher says yes but he is a goober so I don't know(3 votes)

- i don't really get it why in the last exercise the slope is -3/2 you ad plus 2 for the change in x but minus 3 for the change in y.(9 votes)
- I can't understand how to graph an equation with a fraction y-intercept. Ex: y=2x-1/2(5 votes)
- Put a point at (0, -1/2). It is half-way between 0 and -1.

Since the slope is 2, you move up 2 units and right 1.

-- Up 1 unit takes you to 1/2, up 2 units takes you to 1 1/2 (halfway between 1 and 2).

-- Then, go right 1 unit. You should now be at the point 1 1/2, 1)

Hope this helps.(11 votes)

- what if the question is y=x+4(4 votes)
- Remember, "x" is the same as "1x". So, the slope of the equation is 1 and the y-intercept is (0,4).

Hope this helps.(9 votes)

- what is the difference between zero slope and no slope.(1 vote)
- Zero slope means the slope is defined as zero, but no slope means the slope is undefined. A horizontal line has zero slope, but a vertical line has no slope.

Have a blessed, wonderful day!(12 votes)