Linear equations review 11/4 & 11/7

Front

What is the definition of slope in a linear equation?

Back

The slope of a linear equation is a measure of the steepness or incline of the line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you determine if a slope is positive, negative, or zero?

Back

A slope is positive if the line rises from left to right, negative if it falls from left to right, and zero if the line is horizontal.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Front

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

Back

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

Front

How can you find the y-intercept from the equation of a line in slope-intercept form (y = mx + b)?

Back

In slope-intercept form, the y-intercept is represented by the value of b.

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

How do you convert the standard form of a linear equation (Ax + By = C) to slope-intercept form (y = mx + b)?

Back

To convert to slope-intercept form, solve for y: isolate y on one side of the equation.

Front

What is the significance of a negative slope in a real-world context?

Back

A negative slope indicates an inverse relationship between the variables, meaning as one variable increases, the other decreases.

Front

How do you find the y-intercept from the standard form of a linear equation?

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.