Understanding Line Equations from Two Points

This video tutorial explains how to find the equation of a line given two points. It begins by calculating the slope using the formula (y2-y1)/(x2-x1). The tutorial then demonstrates how to use the point-slope formula, y-y1=m(x-x1), to derive the line equation. A practice example is provided, where the slope is calculated and the point-slope formula is applied to find the line equation in both standard and slope-intercept forms. The video concludes with a summary of the key steps and concepts covered.

What is the first step in finding the equation of a line given two points?

• Calculate the y-intercept

• Find the midpoint

• Calculate the slope

• Determine the x-intercept

Which formula is used to calculate the slope of a line?

• m = (y1 + y2) / (x1 + x2)

• m = (x1 + x2) / (y1 + y2)

• m = (y2 - y1) / (x2 - x1)

• m = (x2 - x1) / (y2 - y1)

In the point-slope formula, what does 'm' represent?

• The midpoint

• The slope

• The x-coordinate

• The y-intercept

What is the result of distributing 2 in the equation y - 1 = 2(x + 2)?

• 2x + 4

• x - 2

• 2x - 4

• x + 2

What is the slope of the line passing through the points (-3, 5) and (2, 1)?

• 4/5

• -5/4

• -4/5

• 5/4

How do you eliminate fractions in the equation y - 5 = -4/5(x + 3)?

• Multiply everything by 5

• Multiply everything by 4

• Divide everything by 4

• Divide everything by 5

What is the standard form of the equation 5y = -4x + 13?

• 5x - 4y = 13

• 4x + 5y = 13

• 5x + 4y = 13

• -4x + 5y = 13

In the slope-intercept form y = mx + b, what does 'b' represent?

• The midpoint

• The slope

• The x-intercept

• The y-intercept

What is the slope-intercept form of the equation 5y = -4x + 13?

• y = 4/5x + 13/5

• y = -4/5x + 13/5

• y = 5/4x - 13/5

• y = -5/4x - 13/5

What is the y-intercept in the equation y = -4/5x + 13/5?

• -13/5

• 13/5

• 4/5

• -4/5