Learn how to graph lines whose equations are given in the slope-intercept form y=mx+b.
Graphing lines with integer slopes
Let's graph .
Recall that in the general slope-intercept equation , the slope is given by and the -intercept is given by . Therefore, the slope of is and the -intercept is .
In order to graph a line, we need two points on that line. We already know that is on the line.
Additionally, because the slope of the line is , we know that the point is also on the line.
A coordinate plane. The x- and y-axes each scale by one. The graph of a line goes through the points zero, three and one, five. Both of these points are plotted and labeled.
Check your understanding
Graphing lines with fractional slope
Let's graph .
As before, we can tell that the line passes through the -intercept , and through an additional point .
While it is true that the point 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 , increasing by units will cause to increase by units.
This gives us the additional point .
A coordinate plane. The x- and y-axes each scale by one. The graph of a line goes through the points zero, three and two, zero. Both of these points are plotted and labeled.
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(22 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 positive
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.(32 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.(32 votes)
- How do I graph a line if the slope isn't provided? Here is what I mean:
How do I graph it if I do not know the slope? Thanks!(12 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!(6 votes)
- I don't have a clue on how to do this(8 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.(9 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.(8 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)
- Someone please help me. Im not undertsnding(6 votes)
- Okay so, for example, the question,
y=1/3x - 2
is a demonstration of the Slope-Intercept Form. Which is written,
y=mx + b
the -2 is obviously b which is the y-intercept. You would graph -2 as (0,-2). You would go 3 left and 1 up. Or better known as rise/run. And you would continue to get the line, by connecting the dots. Hope that helped you!(1 vote)
- Not a question. I'm confused on all of this. Not 1 specific part, all of it.(5 votes)