Finding the Equation of a Line from Two Points

The video tutorial explains how to determine the equation of a line passing through two given points. It covers both point slope form and slope intercept form. The process begins with calculating the slope using the formula M = (Y2 - Y1) / (X2 - X1). The tutorial then demonstrates how to write the equation in point slope form using either of the given points. Finally, it shows how to convert the point slope form into slope intercept form by solving for Y.

What is the first step in determining the equation of a line passing through two points?

• Finding the y-intercept

• Calculating the slope

• Identifying the midpoint

• Determining the x-intercept

Which formula is used to calculate the slope between two points?

• M = (X2 - X1) / (Y2 - Y1)

• M = (Y2 - Y1) / (X2 - X1)

• M = (Y1 + Y2) / (X1 + X2)

• M = (X1 + X2) / (Y1 + Y2)

What is the slope of the line passing through the points (1, 1) and (5, -1)?

• -2

• 2

• -1/2

• 1/2

In the point-slope form of a line, what does X1 and Y1 represent?

• The x-intercept

• The y-intercept

• Any point on the line

• The slope of the line

Which of the following is a correct point-slope form equation using the point (1, 1) and slope -1/2?

• Y - 1 = -1/2(X + 1)

• Y + 1 = -1/2(X - 1)

• Y - 1 = -1/2(X - 1)

• Y + 1 = -1/2(X + 1)

What is the point-slope form equation using the point (5, -1) and slope -1/2?

• Y + 1 = -1/2(X + 5)

• Y - 1 = -1/2(X - 5)

• Y - 1 = -1/2(X + 5)

• Y + 1 = -1/2(X - 5)

What is the next step after writing the point-slope form to convert it to slope-intercept form?

• Add the slope to both sides

• Distribute the slope

• Subtract the slope from both sides

• Multiply both sides by the slope

What is the slope-intercept form of the equation Y - 1 = -1/2(X - 1)?

• Y = 1/2X + 1/2

• Y = -1/2X - 1/2

• Y = 1/2X - 1/2

• Y = -1/2X + 1/2

How is 1 1/2 typically written in slope-intercept form?

• As a mixed number

• As a whole number

• As a decimal

• As an improper fraction

What is the final slope-intercept form of the equation after solving for Y?

• Y = -1/2X + 1

• Y = -1/2X + 3/2

• Y = 1/2X + 3/2

• Y = 1/2X + 1