Approximating Graph Intersections

The video tutorial explains how to approximate the intersection point of two linear equations, f(x) = -7x + 2y = 18 and g(x) = 3x + 2y = 0, by analyzing the differences in Y-values at various X-values. The tutorial concludes that the graphs of f(x) and g(x) are almost equal at x = -2 and likely intersect slightly to the left of this point, around x = -2.3 or -2.5.

What is the primary goal when analyzing the given system of equations?

• To find the exact solution for x and y.

• To determine the slope of the lines.

• To approximate the x value where the graphs intersect.

• To calculate the y-intercept of the lines.

How can we approximate the intersection of the graphs of f(x) and g(x)?

• By plotting the graphs on a coordinate plane.

• By finding the exact y values for each x.

• By comparing the y values at different x values to see where they are closest.

• By calculating the derivative of each function.

At which x value are the y values of f(x) and g(x) closest?

• x = 2

• x = -2

• x = 0

• x = -1

What is the difference in y values at x = -2?

• 19

• 14

• 4

• 1

As x increases, what happens to the distance between the graphs of f(x) and g(x)?

• The distance fluctuates randomly.

• The distance decreases.

• The distance remains the same.

• The distance increases.

Where is the intersection of f(x) and g(x) likely to occur relative to x = -2?

• At x = 0

• To the left of x = -2

• Exactly at x = -2

• To the right of x = -2

What is the estimated x value where f(x) and g(x) might intersect?

• x = -2.8

• x = -2.3

• x = -3

• x = -1.5