Functions, slope

Front

What does the 'm' represent in the equation y=mx+b?

Back

The 'm' represents the slope of the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, the value of y increases by 2 units, making the line steep.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

In the context of a real-world scenario, what does a slope of 2 feet per second represent?

Back

It represents that for every second that passes, the height increases by 2 feet.

Front

How do you interpret a negative slope in a real-world context?

Back

A negative slope indicates a decrease in the value of y as x increases, representing a downward trend.

Front

Given the points (2, 4) and (6, 12), how do you find the slope?

Back

Use the formula m = (y2 - y1) / (x2 - x1) to find the slope, which is 2.

Front

What is the significance of the y-intercept in the equation y=mx+b?

Back

The y-intercept (b) is the value of y when x is 0, indicating where the line crosses the y-axis.

Front

If Mrs. Taylor was 10 feet off the ground at 0 seconds and 20 feet at 5 seconds, how do you find her rate of ascent?

Back

Calculate the slope: (20 - 10) / (5 - 0) = 2 feet per second.