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## Integrated math 1

### Course: Integrated math 1>Unit 4

Lesson 4: x-intercepts and y-intercepts

# Intercepts from a table

Sal finds the y-intercept of the graph of a linear function given a table of values. 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!
• 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?"
• An easy way to think about it is, the line is "intercepting the axis at that point." Like a football player intercepting a pass, he or she must cross the path of the ball to intercept it at a certain point.
• 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.
• 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.
• 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.
• Then it's not proportional. That doesn't really make any major difference.
• 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.