Finding the Connections CC3 Ch 4

Front

What is the growth (slope) in the equation y = mx + b?

Back

The growth (slope) 'm' represents the rate of change of y with respect to x, indicating how much y increases or decreases as x increases.

Front

What does the y-intercept represent in the equation y = mx + b?

Back

The y-intercept 'b' is the value of y when x is 0, representing the point where the line crosses the y-axis.

Front

If the equation of a line is y = 2x + 3, what is the y-intercept?

Back

The y-intercept is 3.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line with a slope of 4 and a y-intercept of 10?

Back

The equation is y = 4x + 10.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the equation for a line that passes through the point (0, 2) with a slope of 1?

Back

The equation is y = 1x + 2 or y = x + 2.

Front

How can you determine if a line is increasing or decreasing from its equation?

Back

If the slope 'm' is positive, the line is increasing; if 'm' is negative, the line is decreasing.

Front

What is the significance of the equation y = -2x + 5?

Back

This equation represents a line with a slope of -2 and a y-intercept of 5, indicating it decreases as x increases.

Front

How do you find the value of y when x = 0 in the equation y = 3x + 4?

Back

Substituting x = 0 gives y = 3(0) + 4 = 4, so the y-intercept is 4.