Slope, Intercepts, and Line Intersections

The video tutorial explains how to solve line equations using intercept form. It begins with an introduction to the equation y = mx + b, highlighting the importance of the y-intercept and slope. Two examples are provided: the first involves solving line intersections with given equations, while the second demonstrates rewriting equations into slope-intercept form before graphing and finding solutions. The tutorial emphasizes understanding the relationship between rise and run in determining slope and how to graphically represent these equations to find intersection points.

What is the general form of the equation of a line?

• y = ax + b

• y = ax^2 + bx + c

• y = mx + b

• y = a/x + b

In the equation y = mx + b, what does 'b' represent?

• The slope of the line

• The y-intercept

• The x-intercept

• The origin

How is the slope 'm' of a line defined?

• Run over rise

• Rise over run

• Sum of x and y

• Difference of x and y

What is the y-intercept of the first line in Example 1?

• -5

• 3

• -2

• 5

What is the slope of the first line in Example 1?

• 2/3

• -2/3

• 3/2

• -3/2

Where do the two lines intersect in Example 1?

• (1, 3)

• (-1, -3)

• (-3, -1)

• (3, 1)

What is the first step in rewriting the first equation in Example 2?

• Add 2x to both sides

• Subtract 2x from both sides

• Divide both sides by 2

• Multiply both sides by 2

What is the slope of the line after rewriting the first equation in Example 2?

• -1/2

• -2

• 1/2

• 2

What is the y-intercept of the second line in Example 2?

• 1

• -1

• 0

• 2

What is the slope of the second line in Example 2?

• 1

• -2

• -1

• 2