Comfirming Solutions to Linear Equations

Front

What is a solution to a linear equation?

Back

A solution to a linear equation is an ordered pair (x, y) that makes the equation true.

Front

What does the equation y = 2x - 7 represent?

Back

It represents a linear relationship where y changes based on the value of x, with a slope of 2 and a y-intercept of -7.

Front

How do you confirm if a point is a solution to a linear equation?

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on a coordinate plane.

Front

What is the slope of the line represented by the equation y = 2x - 7?

Back

The slope is 2, which means for every 1 unit increase in x, y increases by 2 units.

Front

What is the y-intercept of the equation y = 2x - 7?

Back

The y-intercept is -7, which is the point where the line crosses the y-axis.

Front

Is (2, -3) a solution to the equation y = 2x - 7?

Back

Yes, substituting x = 2 gives y = 2(2) - 7 = -3.

Front

Is (1, 3) a solution to the graphed equation y = 2x - 7?

Back

Yes, substituting x = 1 gives y = 2(1) - 7 = -5, which does not match 3.

Front

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

Back

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

Front

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

Back

No, substituting x = 5 and y = 5 gives 5 + 5 = 10, which does not equal 12.