Finding Intersection of Linear Functions

This video tutorial demonstrates how to find the point of intersection of two linear functions. Initially, the problem is introduced, highlighting the difficulty of graphing due to fractional intercepts. The solution is approached algebraically by setting the functions equal and solving for X. Fractions are cleared using the least common multiple, and the equation is simplified to find the X coordinate. The corresponding Y coordinate is calculated using one of the original functions. The solution is verified graphically, confirming the accuracy of the algebraic method.

Why is it challenging to graph the intersection of the given linear functions?

• The lines are vertical.

• The x-intercept is a fraction.

• The y-intercept is a fraction.

• The lines are parallel.

What is the first step in finding the intersection of the two functions algebraically?

• Graph the functions.

• Set the functions equal to each other.

• Calculate the slope.

• Find the y-intercept.

What is the least common denominator used to clear fractions in the equation?

• 2

• 10

• 5

• 20

After clearing fractions, what is the next step in solving the equation?

• Multiply both sides by 10.

• Divide both sides by 2.

• Add 16x to both sides.

• Subtract 16x from both sides.

What is the x-coordinate of the intersection point?

• 6

• 9

• 3

• 12

How do you find the y-coordinate once you have the x-coordinate?

• Substitute x into one of the original functions.

• Use the slope of the line.

• Use the midpoint formula.

• Graph the function again.

What is the y-coordinate of the intersection point?

• 5

• 10

• 26/5

• 7/10

Why is it beneficial to verify the solution graphically?

• To determine the x-intercept.

• To find the slope of the line.

• To check for calculation errors.

• To simplify the equation.

What does the graphical verification show about the y-coordinate?

• It is exactly 5.

• It is slightly more than 5.

• It is less than 5.

• It is exactly 10.

What would have been difficult if the problem was solved only graphically?

• Finding the x-coordinate.

• Determining the y-coordinate accurately.

• Locating the y-intercept.

• Identifying the slope.