Understanding Linear Equations and Graphs

The video tutorial explains how to solve a system of equations by graphing. It covers three possible outcomes when graphing two lines: one solution, no solution, or infinite solutions. The tutorial demonstrates graphing the equations 2x + y = 4 and x - y = 2, finding their intersection point, and verifying the solution by substitution.

What are the possible outcomes when graphing two lines on a coordinate plane?

• One solution, two solutions, or infinite solutions

• No solution, two solutions, or infinite solutions

• Two solutions, no solution, or infinite solutions

• One solution, no solution, or infinite solutions

What is the slope-intercept form of a linear equation?

• x = by + m

• y = mx + b

• x = my + b

• y = bx + m

How do you determine the slope from the equation y = -2x + 4?

• The slope is -2

• The slope is 4

• The slope is 2

• The slope is -4

What is the y-intercept of the equation y = -2x + 4?

• (0, 4)

• (4, 0)

• (2, 0)

• (0, -2)

How can you graph the equation x - y = 2?

• By using the midpoint formula

• By creating a table of values

• By finding the vertex

• By using the quadratic formula

What is the slope of the line determined by the points (2, 0) and (3, 1)?

• 1

• 0

• -1

• 2

What does the intersection point of two lines represent in a system of equations?

• The y-intercept of the lines

• The solution to the system

• The midpoint of the lines

• The average of the slopes

What is the solution to the system of equations given in the video?

• (1, 1)

• (3, 1)

• (0, 2)

• (2, 0)

How can you verify that a point is a solution to a system of equations?

• By substituting the point into both equations

• By checking if the point lies on the x-axis

• By finding the midpoint of the point

• By calculating the distance from the origin

What is the result of substituting x = 2 and y = 0 into the equation 2x + y = 4?

• 0 = 4

• 2 = 4

• 4 = 4

• 4 = 2