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### Course: Algebra 1>Unit 4

Lesson 4: x-intercepts and y-intercepts

# Intercepts from a table

The y-intercept is the y-coordinate when x=0, and the x-intercept is the x-coordinate when y=0. The y-intercept is not in the table. Since the table represents a line, there's a constant rate of change of y with respect to x. So we can find that pattern and fill in skipped values from the table to find the y-intercept. Created by Sal Khan.

## Want to join the conversation?

• The thing is, it's easy to understand here, but when you actually start the practice, it's totally different.
• SAL's question, -2,8 1,2 2,0 4,-4

MY question 135,96 34,68 56,34 -96,-87

(Not a real question BTW. just emphasizing)
• What is function? We did not learn about it yet.
• A function is a rule where each input is assigned to one, and only one, output. There are many kinds of functions; even the rule "Assign every word to the number of syllables it has" is a function.

But the kind of function we are talking about here is a line. In a graphed line, each x corresponds to only one y. Also the rate of x change to the rate of y change is the same (because it is straight).

So you can use this rule to determine intercepts in a line.

For more on functions, see https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:evaluating-functions/v/what-is-a-function.

Hope this helps!!
• Is there any way to find intercept x ( or y) if we cannot get the other intercept to zero by following the table method?
In all the questions, if we need to find intercept x/y, the other intercept always perfectly reaches to zero.
• If the table doesn't directly go to 0, you could always get the equation of the line described by the table and then plug in 0 for x to get the y-int, or 0 for y to get x-int. To get the equation of a line from a table, you need to determine the slope of the line by calculating the ratio of the change in y-value to the change in x-value. For example, if two points in the table were (1, 2) and (4, 8), you could see that the y value changed by 6 and the x value changed by 3. This would give you a slope of 2 through 6 / 3 = 2. You can then plug a data set for a point into the linear slope-intercept equation: y = mx + b. Going with the numbers from the previous example, let's say I plugged in (1,2). Since m is the slope, my equation would look a little something like this:
2 = 2*1 + b
From there, we can solve for b, and see that b = 0:
2 = 2 + b
2 - 2 = 2 + b - 2
0 = b
Since b is 0, our completed equation looks like this:
y = 2x + 0
To find the intercepts of this equation, we just substitute a 0 in the right place. To find the y-intercept, plug in a 0 for x:
y = 2*0 + 0
y = 0
And for the x-intercept:
0 = 2x + 0
0/2 = 2x/2
0 = x

Hope this helped!
• What if there is a straight line and it never passes through one of the axis? Just curious.
• It really depends on the slope. When the slope is zero, the line is horizontal and there is no x-intercept (but then sometimes the line is right over the axis). If the slope is undefined, there is no y-intercept.
• i am confused at . why does the -1/2 mean?
• As x increases by 1, y decreases by 2. It doesn't matter if the rate of change is -1/2 or 1/-2. They are both the same value.
• so what about the x- intercept also that is being asked in the practice intercept from a table......
• Well its pretty much the same thing, you're just solving for X instead of Y.
• What if your table is going down (or up) by a number that will miss zero?
If I have, say, 8 on the x side, but my table is decreasing every 15, then my next input would miss zero and go to -5! What do I do there?

This is implying that the other side cannot be divided by said number.
• You might already have an answer by now, but in your case, you would find out the slope, then the equation of the line and then input one pair of coordinates into 'x' and 'y'. Say 'y' is 10. So then it would become: 10=slope*8+b. b is the constant aka y-intercept which is what we need to find. So then you would solve for b.

Hope that helped!
• Why is it when the line crosses y it is the y-intercept?? why dont we just call it "the time the line crosses the y-axis?"