Solutions to Linear Equations

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 ax + by = c, where a, b, and c are constants.

Front

What does it mean for a point to be a solution to a linear equation?

Back

A point (x, y) is a solution to a linear equation if, when the x and y values are substituted into the equation, the equation holds true.

Front

Is (3, 1) a solution to the linear equation 4x + 3y = 12?

Back

No

Front

Is (5, 5) a solution to the linear equation x + y = 12?

Back

No

Front

Which of the following is a solution to the equation 2x + 3y = 12: (0, 3), (3, 2), (2, 0), (-1, -4)?

Back

(3, 2)

Front

Given the equation 3x + y = 5 and x = 1, what is the value of y?

Back

2

Front

Which of these is a solution to the equation 3y - 2x = -3: (6, 3), (5, 9)?

Back

(6, 3)

Front

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

Back

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

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 as (0, b) in the equation y = mx + b.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).