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

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-value is substituted into the equation, the resulting y-value is equal to the y-value of the point.

Front

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

Back

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

Front

How do you determine if a point is a solution to the equation y - 12 = x?

Back

Substitute the x-value of the point into the equation and check if the resulting y-value equals the y-value of the point.

Front

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

Back

The y-intercept is -7, which is the value of y when x = 0.

Front

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

Back

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

Front

How can you check if (0, 12) is a solution to the equation y - 12 = x?

Back

Substituting x = 0 into the equation gives y - 12 = 0, which simplifies to y = 12, confirming that (0, 12) is a solution.

Front

What does the equation 5x - y = -12 represent?

Back

It represents a linear relationship between x and y, which can be rearranged to slope-intercept form.

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.

Front

How do you find the solution to the equation 4x + 3y = 12?

Back

You can substitute values for x or y and solve for the other variable, or rearrange the equation to find y in terms of x.