Equations and Linear Graphs

Front

What is the graph of the equation y = 2x + 3?

Back

The graph of the equation y = 2x + 3 is a straight line.

Front

How do you find the slope of a line given 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 of the line passing through the points (3, 7) and (6, 10)?

Back

The slope is 1.

Front

How do you solve the equation 2(4x - 3) = 10?

Back

First, distribute: 8x - 6 = 10. Then, add 6 to both sides: 8x = 16. Finally, divide by 8: x = 2.

Front

What is the equation of a line with slope 2 and y-intercept 4?

Back

The equation is y = 2x + 4.

Front

What is the slope of the line passing through the points (-1, 3) and (5, -1)?

Back

The slope is -2/3.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.

Front

What is the difference between a linear equation and a quadratic equation?

Back

A linear equation represents a straight line, while a quadratic equation represents a parabola.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope.