Equations of Lines: Slope and Y-Intercept Insights

What is the main focus of this lesson?

• Equations of circles

• Equations of curves

• Equations of lines passing through the origin

• Equations of lines not necessarily passing through the origin

What is the form of the equation for lines passing through the origin?

• y = b

• y = mx

• y = x + b

• y = mx + b

If a line has a slope of 2/3, what does this mean in terms of change in Y and change in X?

• For every 3 units increase in X, Y increases by 2 units

• For every 2 units increase in X, Y increases by 3 units

• For every 2 units increase in Y, X increases by 3 units

• For every 3 units increase in Y, X increases by 2 units

Which line is steeper if one has a slope of 2/3 and the other has a slope of 3?

• Both lines are equally steep

• The line with a slope of 3

• Cannot be determined

• The line with a slope of 2/3

What is the equation of a line with a slope of 3 that passes through the origin?

• y = x + 3

• y = 3

• y = 3x + 1

• y = 3x

Why can the slope of a line be determined even if it does not pass through the origin?

• Because the slope is always one

• Because the slope is always zero

• Because the line must pass through the origin

• Because slope is about the ratio of changes in Y and X

What is true about each point on line B compared to the equivalent point on y = 3/4x?

• Each point on line B is 4 units below the equivalent point

• Each point on line B is 4 units above the equivalent point

• Each point on line B is 3 units below the equivalent point

• Each point on line B is 3 units above the equivalent point

What is the y-intercept of the line y = 1/2x + 3?

• 2

• 3

• 1

• 0

How do you determine the slope of a line from its equation in slope-intercept form?

• It is the number added to x

• It is the number multiplying x

• It is the constant term

• It is the y-intercept

What does the y-intercept represent in the equation of a line?

• The change in Y for a given change in X

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

• The slope of the line

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