Understanding Linear Equations

What is the slope-intercept form of a linear equation?

• y = m(x - x1) + y1

• y - y1 = m(x - x1)

• y = m(x2 - x1) + b

• y = mx + b

In the slope-intercept form, what does the constant 'b' represent?

• The y-coordinate where the line crosses the y-axis

• The x-coordinate of a point on the line

• The slope of the line

• The x-intercept of the line

When is the point-slope form of a linear equation most useful?

• When the line is vertical

• When the slope and a point on the line are known

• When two points on the line are known

• When the slope and y-intercept are known

What is the general form of the point-slope equation?

• y = mx + b

• y - y1 = m(x - x1)

• y = m(x - x2) + y2

• y = m(x2 - x1) + b

What information is needed to use the two-point form of a linear equation?

• Two distinct points on the line

• The slope and y-intercept

• The x-intercept and y-intercept

• The slope and a point on the line

How is the slope calculated in the two-point form?

• Using the formula m = (x1 - x2) / (y1 - y2)

• Using the formula m = (y2 - y1) / (x2 - x1)

• Using the formula m = (y1 - y2) / (x1 - x2)

• Using the formula m = (x2 - x1) / (y2 - y1)

In the example provided, what are the coordinates of the first point used?

• (3, 5)

• (7, 8)

• (5, 3)

• (8, 7)

Why can't the two-point form be used to describe a vertical line?

• Because the line does not intersect the y-axis

• Because the y-coordinates of the points are the same

• Because the x-coordinates of the points are the same

• Because the slope is zero

What happens if x1 and x2 are equal in the two-point form?

• The equation becomes undefined

• The slope becomes zero

• The line becomes horizontal

• The y-intercept becomes zero

What will be introduced in the next lecture?

• The standard form

• The two-point form

• The point-slope form

• The slope-intercept form