Writing Linear Equations from Graphs

The video tutorial explains how to write linear equations from graphs using the slope-intercept form. It covers six examples, each illustrating different scenarios such as positive and negative slopes, zero slope, and undefined slope. The tutorial emphasizes understanding the rise and run to calculate the slope and how to identify the y-intercept. It also explains how to handle cases where the slope is zero or undefined, resulting in horizontal or vertical lines, respectively.

What does the y-intercept represent in a linear equation?

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

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

• The slope of the line

• The maximum value of y

If the slope of a line is 1/2, what does this indicate about the line's increase?

• Decreases by 1 unit of y for every 2 units of x

• Decreases by 2 units of y for every 1 unit of x

• Increases by 2 units of y for every 1 unit of x

• Increases by 1 unit of y for every 2 units of x

How do you calculate the slope of a line from two points (x1, y1) and (x2, y2)?

• (y2 - y1) / (x2 - x1)

• (x2 - x1) / (y2 - y1)

• (y1 - y2) / (x1 - x2)

• (x1 - x2) / (y1 - y2)

What is the equation of a line with a slope of -1/2 and a y-intercept of 1?

• y = -1/2x - 1

• y = 1/2x + 1

• y = 1/2x - 1

• y = -1/2x + 1

What does a negative slope indicate about the direction of a line?

• The line moves upwards to the left

• The line moves downwards to the right

• The line moves downwards to the left

• The line moves upwards to the right

In the context of the video, what does a slope of zero signify about a line?

• The line is increasing

• The line is decreasing

• The line is vertical

• The line is horizontal

What is the equation of a line that has a slope of 2 and passes through the point (0, -1)?

• y = 2x + 1

• y = 2x - 1

• y = -2x - 1

• y = -2x + 1

If a line's equation is y = 0x - 2, what is the y-value for any x?

• 0

• 2

• Undefined

• -2

What does an undefined slope in a graph typically represent?

• A horizontal line

• A line decreasing at a constant rate

• A line increasing at a constant rate

• A vertical line

What is the equation for a vertical line passing through x = 3?

• x = -3

• y = -3

• x = 3

• y = 3