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, indicating how steep the line is.

Front

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

Back

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

Front

How can you determine the y-intercept from the equation y = mx + b?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

Convert the equation 4y = 8x - 16 to slope-intercept form.

Back

The slope-intercept form is y = 2x - 4.

Front

What is the slope of the equation y = -3x + 4?

Back

The slope of the equation y = -3x + 4 is -3.

Front

Write the linear equation for the following scenario: 'A taxi charges a base fare of $3 and $2 for each mile driven.'

Back

y = 2x + 3, where y is the total fare and x is the number of miles.

Front

If a line has a slope of 2, what does this indicate about the line's steepness?

Back

A slope of 2 indicates that for every 1 unit increase in x, y increases by 2 units, making the line steep.