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

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. This simplifies to 3 + 13y = 39, leading to 13y = 36, so y = 36/13.

Front

What is the solution to the equation 3x + y = 5 when x = 1?

Back

Substituting x = 1 gives: 3(1) + y = 5, which simplifies to 3 + y = 5. Therefore, y = 2.

Front

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

Back

No, substituting (5, 5) gives 5 + 5 = 10, which does not equal 12.

Front

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

Back

No, substituting (3, 1) gives 4(3) + 3(1) = 12 + 3 = 15, which does not equal 12.

Front

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

Back

Yes, substituting (1, 2) gives 2(1) + 5(2) = 2 + 10 = 12, which equals 12.

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 the equation y = 2x + 3?

Back

The y-intercept is 3, which is the value of y when x = 0.

Front

How can you determine if two linear equations are parallel?

Back

Two linear equations are parallel if they have the same slope but different y-intercepts.