#22. Find the Equation of the Line that is Parallel to the x + 4y = 8 and Passes Through (1, 4)

TL;DR

Finding the equation of a line parallel to X+4y=8 passing through point (3,-1).

Transcript

let's workout problem number 22 find the equation of the line that is parallel to the line X plus 4y equals 8 so we have X plus 4y equals 8 so our line is parallel to this line and passes through the point 3 comma negative 1 so we're given the point so we have to find the equation of the line that's parallel to this line here and passes through thi... Read More

Key Insights

• 🫥 Parallel lines have the same slope, ensuring consistency in their directional inclinations.
• 🫥 Calculating the slope of a line is crucial in determining its characteristics and relationship with other lines.
• 😥 The point-slope formula simplifies the process of finding the equation of a line passing through a given point.

Questions & Answers

Q: How do you determine the slope of a line parallel to a given equation?

To find the slope of a line parallel to a given equation, rearrange the equation to y=mx+b form, where m is the slope of the line.

Q: What is the significance of parallel lines having the same slope?

Parallel lines have the same slope, which means they have the same steepness and will never intersect no matter how far they extend.

Q: How is the point-slope formula used to find the equation of a line?

The point-slope formula, y-y1=m(x-x1), helps determine the equation of a line passing through a specific point with a given slope.

Q: Why is it important to multiply by four to get rid of fractions in the equation?

Multiplying by four helps eliminate fractions, making calculations easier and allowing for a simplified form of the equation without fractional coefficients.

Summary & Key Takeaways

• Given a line equation X+4y=8, determine the equation of a parallel line passing through point (3,-1).

• Calculate the slope of the line by rearranging the equation to y=(-1/4)X+2.

• Utilize the point-slope formula to find the final equation of the parallel line: y=(-1/4)X-1/4.