Understanding Slope and Intersections

The video tutorial explains how to determine if a coordinate point is a solution to a system of equations by graphing. It covers converting equations to the slope-intercept form, graphing them on a coordinate plane, and finding the intersection point. The tutorial concludes by verifying the solution through substitution.

What is the purpose of graphing two equations on a coordinate plane?

• To find the y-intercept of each equation

• To identify the intersection point as the solution

• To calculate the distance between the lines

• To determine the slope of each line

What is the first step in converting an equation to the slope-intercept form?

• Multiply both sides by -1

• Add y to both sides

• Divide both sides by x

• Subtract x from both sides

In the equation y = x + 3, what does the number 3 represent?

• The slope of the line

• The x-intercept

• The y-intercept

• The intersection point

What is the slope of the line represented by the equation y = x + 3?

• 0

• -1

• 3

• 1

How is the slope of the line y = x - 5 described?

• Undefined

• Positive one

• Zero

• Negative one

What is the y-intercept of the equation y = x - 5?

• 0

• -5

• 5

• 1

Where do the lines y = x + 3 and y = x - 5 intersect?

• (4, -1)

• (3, 3)

• (-1, 4)

• (0, 0)

What does the intersection point of two lines on a graph represent?

• The average slope of the lines

• The solution to the system of equations

• The y-intercept of the lines

• The midpoint of the lines

If x = 4 and y = -1, which equation is satisfied?

• y = x + 5

• y = x - 3

• y = x - 5

• y = x + 3

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

• By checking if it lies on the x-axis

• By substituting the point into both equations

• By ensuring the point is the y-intercept

• By finding the midpoint of the lines