Semester 1 Linear Functions Review

Front

What is the definition of slope in a linear function?

Back

The slope of a linear function is a measure of the steepness of the line, calculated as the change in the y-coordinate divided by the change in the x-coordinate between two points on 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

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

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

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 determine the y-intercept from a linear equation in slope-intercept form?

Back

In the equation y = mx + b, the y-intercept is the value of b.

Front

What is the significance of a negative slope in a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the relationship between the slope and parallel lines?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between the slope and perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one line has a slope of m, the other will have a slope of -1/m.

Front

How can you find the equation of a line given its slope and a point on the line?

Back

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.