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.