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

Is (1, 2) a solution to the linear equation 2x + 5y = 12?

Back

Yes

Front

How do you find the value of y in the equation 3x + 13y = 39 when x = 1?

Back

Substitute x = 1 into the equation: 3(1) + 13y = 39, then solve for y to get y = 36/13.

Front

What is the value of y in the equation 3x + y = 5 when x = 1?

Back

Substitute x = 1 into the equation: 3(1) + y = 5, then solve for y to get y = 2.

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 slope of the line represented by the equation 2x + 3y = 6?

Back

To find the slope, rewrite the equation in slope-intercept form: 3y = -2x + 6, then y = -2/3x + 2. The slope is -2/3.

Front

What is the y-intercept of the equation y = 4x + 1?

Back

The y-intercept is the value of y when x = 0. Here, it is 1.