Finding the x-intercept of a line | Algebra I | Khan Academy

Summary

This 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

00:00

🧮 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.

Keywords

💡x-intercept

The x-intercept is the point where a line crosses the x-axis on a graph, meaning the y-coordinate at that point is zero. In the video, the narrator explains that the x-intercept is found by setting y to 0 in the given equation and solving for x, which results in an x-intercept of 7/3.

💡y equals 0

In this context, 'y equals 0' refers to the condition required to find the x-intercept of a line. By setting the y-coordinate to 0, the narrator isolates x in the equation 2y + 3x = 7, making it possible to solve for the exact value of the x-intercept.

💡graph

A graph is a visual representation of mathematical equations, showing relationships between variables. In the video, the graph represents the line formed by the equation 2y + 3x = 7, and it's used to visually estimate where the line crosses the x-axis.

💡equation

An equation is a mathematical statement that asserts the equality of two expressions. The narrator uses the equation 2y + 3x = 7 to demonstrate how to find the x-intercept by manipulating the equation when y is set to 0.

💡7/3

The value 7/3 represents the x-coordinate of the x-intercept. It is derived from solving the equation 3x = 7. The narrator breaks down the fraction to explain that it equals 2 and 1/3, connecting it to the visual estimate of the graph.

💡improper fraction

An improper fraction is a fraction where the numerator is greater than the denominator. In the video, 7/3 is an example of an improper fraction, and the narrator suggests using this form when entering the answer into a program like Khan Academy.

💡divide both sides

Dividing both sides refers to the algebraic process used to isolate a variable. In this case, the narrator divides both sides of the equation 3x = 7 by 3 to solve for x, demonstrating a key step in solving for the x-intercept.

💡x-axis

The x-axis is the horizontal axis in a coordinate plane. In the video, the narrator explains that the x-intercept is the point where the line crosses the x-axis, which happens when the y-coordinate is zero.

💡estimate

Estimation involves making a rough calculation or educated guess. The narrator initially estimates the x-intercept by observing the graph and noting that the value looks to be a little over 2, then confirms the exact value through calculation.

💡solve for x

Solving for x is the process of determining the value of the variable x in an equation. In the video, the narrator solves for x by first setting y to 0 and then performing algebraic manipulations to find that x equals 7/3, which is the x-intercept.

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.