Linear equations - Algebra 1

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

Write the equation for a line with a slope of 2 and a y-intercept of 3.

Back

y = 2x + 3

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, represented as (-∞, ∞).

Front

How do you evaluate a function at a given point?

Back

To evaluate a function f(x) at a point x = a, substitute a into the function and simplify.

Front

What is the equation for the total cost of renting a car for x days with a one-time fee of $22.75 and a daily fee of $32.50?

Back

y = 22.75 + 32.50x

Front

If a tree grows 3 inches per week and was initially 10 inches tall, what is the equation for its height after x weeks?

Back

y = 3x + 10