Linear equations (one variable)

Front

What is a linear equation in one variable?

Back

A linear equation in one variable is an equation that can be expressed in the form ax + b = 0, where a and b are constants and x is the variable.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

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

Back

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

Front

How do you find the slope (m) from the slope-intercept form?

Back

The slope (m) can be found directly from the equation in the form y = mx + b as the coefficient of x.

Front

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

Back

The y-intercept (b) represents the point where the line crosses the y-axis, which occurs when x = 0.

Front

What is the process to solve for a variable in terms of other variables?

Back

To solve for a variable in terms of others, rearrange the equation using algebraic operations to express the desired variable on one side.

Front

What is the formula to solve for x in the equation (1/w) + (1/y) = (1/x)?

Back

x = (wy)/(w + y).

Front

How do you rearrange the equation y = mx + b to solve for b?

Back

To solve for b, rearrange the equation to b = y - mx.

Front

What is the relationship between the variables in the equation a = b + c?

Back

In the equation a = b + c, c can be expressed as c = a - b.

Front

What is the significance of solving equations for specific variables?

Back

Solving equations for specific variables allows us to express one variable in terms of others, which is essential for understanding relationships between variables.