Point-Slope Form and Y-Intercept Exploration

The video tutorial explains the point-slope form of a linear equation, which is used to write equations using a given slope and a point on the line. It covers the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The tutorial provides examples and exercises on how to write equations in point-slope form, including scenarios where two points are given, requiring the calculation of the slope. It also demonstrates how to derive point-slope form from a table of points and a graphed line.

What is the general formula for point-slope form?

• y = mx + b

• y - y1 = m(x - x1)

• ax + by = c

• y = mx

In the equation y - 2 = 3(x - 4), what is the slope?

• 2

• 4

• 1

• 3

In the equation y + 5 = -2(x + 3), what is the point?

• (-3, 5)

• (3, -5)

• (3, 5)

• (-3, -5)

How would you write the equation of a line that passes through (3, 5) with a slope of 6?

• y + 3 = 6(x + 5)

• y - 3 = 6(x - 5)

• y + 5 = 6(x + 3)

• y - 5 = 6(x - 3)

Given the point (-9, -3) and slope -1/2, what is the correct point-slope form equation?

• y + 3 = 1/2(x + 9)

• y - 3 = 1/2(x - 9)

• y + 3 = -1/2(x + 9)

• y - 3 = -1/2(x - 9)

If a line passes through (6, -7) and has a slope of 1, what is the simplified point-slope form equation?

• y - 7 = x - 6

• y + 7 = x + 6

• y - 7 = x + 6

• y + 7 = x - 6

How do you find the slope between two points (2, 4) and (3, 6)?

• (3 - 2) / (6 - 4)

• (4 - 6) / (2 - 3)

• (2 - 3) / (4 - 6)

• (6 - 4) / (3 - 2)

What is the point-slope form equation for the points (2, 4) and (3, 6)?

• y - 6 = 2(x - 3)

• y - 4 = 2(x - 2)

• y + 6 = 2(x + 3)

• y + 4 = 2(x + 2)

Given the table points (1, -5) and (2, -3), what is the slope?

• -1

• 1

• -2

• 2

From the graph, if the rise is 1 and the run is 3, what is the slope?

• 1/3

• 3

• 1

• 1/2