Finding the x-intercept of a line | Algebra I | Khan Academy
Summary
TLDRThis educational video script explains how to find the x-intercept of a line given by the equation 2y + 3x = 7. The x-intercept is where the line crosses the x-axis, which occurs when y=0. By substituting y=0 into the equation, we find that 3x = 7, leading to x = 7/3. The script further clarifies that 7/3 is equivalent to 2 and 1/3, which is the exact x-intercept. This methodical approach helps in understanding the concept of x-intercepts and their calculation.
Takeaways
- 📐 The script discusses finding the x-intercept of a line given by the equation 2y + 3x = 7.
- 🎯 The x-intercept is where the line crosses the x-axis, which is when y = 0.
- 👀 The script suggests visually estimating the x-intercept to be a little over 2, between 2 and 3, and less than 2.5.
- 🧮 To find the exact x-intercept, set y to 0 in the equation and solve for x.
- 📉 Plugging y = 0 into the equation gives 3x = 7.
- 🔍 Dividing both sides by 3 yields x = 7/3.
- 🔢 The fraction 7/3 is equivalent to 2 and 1/3 when expressed as a mixed number.
- 📝 Another way to understand 7/3 is as 2 full times with a remainder of 1, then dividing the remainder by 3.
- 📚 The script implies that on Khan Academy, it's recommended to input the improper fraction directly.
- 📖 The final answer for the x-intercept is 7/3.
Q & A
What is the definition of an x-intercept?
-The x-intercept is the x value when y is equal to 0, or it's the point where the graph intersects the x-axis.
How can we determine the x-intercept using the equation of the line?
-To find the x-intercept, set y equal to 0 in the equation and solve for x.
What equation is given in the transcript to find the x-intercept?
-The equation given is 2y + 3x = 7.
What is the x-intercept when y is set to 0 in the equation 2y + 3x = 7?
-When y is set to 0, the equation simplifies to 3x = 7. Solving for x gives x = 7/3.
How can 7/3 be interpreted as a mixed number?
-7/3 is the same as 2 and 1/3, because 3 goes into 7 two times, leaving a remainder of 1, which is then divided by 3.
What is another way to understand 7/3 visually?
-You can think of 7/3 as 6/3 plus 1/3, which equals 2 and 1/3.
Why does the speaker suggest using the improper fraction 7/3?
-The speaker suggests using 7/3 because it is easier to input as an answer in Khan Academy exercises.
How does the speaker describe the location of the x-intercept on the graph?
-The speaker estimates that the x-intercept is a little over 2, less than 2 and 1/2, but notes that it's difficult to determine the exact value without calculation.
How do you verify if the x-intercept of 7/3 matches the visual estimation on the graph?
-You can verify by converting 7/3 to 2 and 1/3, which aligns with the visual estimate of being slightly over 2.
What is the value of the x-intercept in decimal form?
-The decimal equivalent of 7/3 is approximately 2.33.
Outlines
🧮 Solving for the X-Intercept of a Line
In this paragraph, the speaker introduces the problem of finding the x-intercept of the line described by the equation 2y + 3x = 7. The x-intercept is defined as the point where the graph intersects the x-axis, meaning y = 0. By visually inspecting the graph, the speaker approximates the x-intercept to be a little over 2 but less than 2.5. However, to find the exact value, the equation is solved algebraically by substituting y = 0 into the equation, resulting in 3x = 7. Solving for x gives x = 7/3, which simplifies to 2 and 1/3. The speaker then relates the value of 7/3 to its mixed fraction form and confirms that this corresponds to the x-intercept. They note that while using a platform like Khan Academy, entering the improper fraction 7/3 is often more straightforward.
Mindmap
Keywords
💡x-intercept
💡y equals 0
💡graph
💡equation
💡7/3
💡improper fraction
💡divide both sides
💡x-axis
💡estimate
💡solve for x
Highlights
The x-intercept is the x value when y is equal to 0.
The x-intercept is where the graph intersects the x-axis.
To find the exact x-intercept, turn to the equation and set y equal to 0.
Substitute y = 0 into the equation 2y + 3x = 7 to solve for x.
After substituting y = 0, the equation simplifies to 3x = 7.
Solve 3x = 7 by dividing both sides by 3, resulting in x = 7/3.
7/3 is the same as 2 and 1/3, which means 3 goes into 7 two times with a remainder of 1.
The x-intercept of the line is 7/3 or 2 and 1/3.
By visual inspection, the x-intercept is a little over 2 and less than 2 and 1/2.
The exact x-intercept of the line is confirmed to be 7/3.
A reminder that 7/3 is the improper fraction representation of the x-intercept.
Using an improper fraction for input, like 7/3, is often easier in exercises such as those on Khan Academy.
The equation simplifies quickly when y = 0, focusing solely on solving for x.
Breaking down fractions like 7/3 helps visualize how they translate to mixed numbers.
The x-intercept's visual approximation on the graph closely matches its calculated value of 2 and 1/3.
Transcripts
The graph of the line 2y plus 3x equals
7 is given right over here.
Determine its x-intercept.
The x-intercept is the x value when y is equal to 0,
or it's the x value where our graph actually
intersects the x-axis.
Notice right over here our y value is exactly 0.
We're sitting on the x-axis.
So let's think about what this x value must be.
Well, just trying to eyeball a little bit,
it's a little over 2.
It's between 2 and 3.
It looks like it's less than 2 and 1/2.
But we don't know the exact value.
So let's go turn to the equation to figure out the exact value.
We essentially have to figure out
what x value, when y is equal to 0,
will have this equation be true.
So we could just say 2 times 0 plus 3x is equal to 7.
Well, 2 times 0 is just going to be 0,
so we have 3x is equal to 7.
Then we can divide both sides by 3 to solve for x,
and we get x is equal to 7/3.
Does that look like 7/3?
Well, we just have to remind ourselves
that 7/3 is the same thing as 6/3 plus 1/3.
And 6/3 is 2.
So this is the same thing as 2 and 1/3.
Another way you could think about it is 3
goes into 7 two times, and then you have a remainder of 1.
So you've still got to divide that 1 by 3.
It's 2 full times and then a 1/3,
so this looks like 2 and 1/3.
And so that's its x-intercept, 7/3.
If I was doing this on the exercise on Khan Academy,
it's always a little easier to type in the improper fraction,
so I would put in 7/3.
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