Slope and y=mx+b

Front

What is the Slope-Intercept Form of a linear equation?

Back

The Slope-Intercept Form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

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

Back

The y-intercept (b) is the value of y when x = 0; it is the point where the line crosses the y-axis.

Front

Given two points (7, -3) and (6, -8), how do you find the equation of the line?

Back

First, calculate the slope using m = (y2 - y1) / (x2 - x1). Then use the point-slope form to find the equation.

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How can you convert the point-slope form to slope-intercept form?

Back

To convert, solve for y to get it in the form y = mx + b.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about the relationship between x and y?

Back

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

Front

How do you find the slope of a line given two points (-4, 7) and (-6, -4)?

Back

Use the formula m = (y2 - y1) / (x2 - x1) to calculate the slope.