Linear Equations Two Variables

Front

What is a linear equation in two variables?

Back

A linear equation in two variables is an equation that can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

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

Back

To find the y-intercept of a linear equation, set x = 0 and solve for y. The y-intercept is the point where the line crosses the y-axis.

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

Convert the equation 5y - 15 = 10x to slope-intercept form.

Back

y = 2x + 3.

Front

What is the y-intercept of the equation y = 4x - 2?

Back

The y-intercept is -2.

Front

Write the linear equation for: 'An electrician has an appointment fee of $250, then charges $75 for each additional hour.'

Back

y = 75x + 250.

Front

Write the linear equation for: 'A car rental company charges a flat fee of $30 plus $0.20 per mile driven.'

Back

y = 0.20x + 30.

Front

What does it mean if the slope of a line is negative?

Back

If the slope of a line is negative, it means that as x increases, y decreases, indicating a downward trend.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept represents the starting value of y when x is zero, often indicating a fixed cost or initial condition in real-world scenarios.