Dilations and Slope

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

How do you find the slope from an equation in slope-intercept form?

Back

In the slope-intercept form of a line, y = mx + b, the slope 'm' is the coefficient of x.

Front

What is the slope of the line represented by the equation y = 9 - 2x?

Back

m = -2.

Front

What is the slope in the equation y = 4x + 3?

Back

m = 4.

Front

How would you write the equation of a line with a slope of 2/3 and a y-intercept of -3?

Back

y = 2/3x - 3.

Front

What is the equation of a line with a slope of 1/3 and a y-intercept of -2?

Back

y = 1/3x - 2.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the effect of a dilation factor greater than 1 on a point's coordinates?

Back

A dilation factor greater than 1 will increase the distance of the point from the origin, effectively enlarging the figure.

Front

What happens to the coordinates of point A(3, 6) under a dilation of 2?

Back

The new coordinates A' will be (6, 12).