Exploring Point-Slope Form in Algebra

The video tutorial explains how to derive the equation of a line using a given slope and a point on the line. It introduces the concept of slope as the change in y over the change in x and uses this to construct the line equation. The tutorial then derives the point-slope form of the equation and demonstrates its application with examples. Finally, it shows how to convert the point-slope form into the more familiar slope-intercept form.

What two pieces of information are given about the line in the problem?

• The x-intercept and the y-intercept

• Two points on the line

• The slope and a point on the line

• The slope and the y-intercept

What does the Greek letter Delta (Δ) represent in the context of slope?

• The ratio of values

• The product of values

• The difference between values

• The sum of values

Tags

CCSS.8.EE.B.5

How is the slope between two points (a, b) and (x, y) calculated?

• (x - a) / (y - b)

• (y - b) / (x - a)

• (a - x) / (b - y)

• (b - y) / (a - x)

Tags

CCSS.8.EE.B.5

What is the point-slope form of the equation derived in the video?

• y + b = m(x - a)

• y + b = m(x + a)

• y - b = m(x + a)

• y - b = m(x - a)

Why is the form y - b = m(x - a) called point-slope form?

• Because it uses the x-intercept and slope

• Because it uses the y-intercept and slope

• Because it uses two points on the line

• Because it uses a point on the line and the slope

Given a line with a slope of 2 passing through the point (-7, 5), what is the point-slope form of its equation?

• y + 5 = 2(x + 7)

• y - 5 = 2(x - 7)

• y + 5 = 2(x - 7)

• y - 5 = 2(x + 7)

How can the expression x - (-7) be simplified?

• x - 7

• x + 7

• x - 14

• x + 14

Tags

CCSS.7.EE.A.1

What is the first step to convert the point-slope form to slope-intercept form?

• Distribute the slope

• Combine like terms

• Subtract b from both sides

• Add b to both sides

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

What is the slope-intercept form of the equation y - 5 = 2(x + 7)?

• y = 2x - 19

• y = 2x - 5

• y = 2x + 19

• y = 2x + 5

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

What does the slope-intercept form of a line equation provide?

• The x-intercept and the slope

• The y-intercept and the slope

• Two points on the line

• The x-intercept and the y-intercept

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3