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 can you determine if a point is a solution to the equation 2x + 3y = 12?

Back

Substitute the x and y values of the point into the equation. If the left side equals the right side, then it is a solution.

Front

What is the solution to the equation 5x - y = -12 when x = -4?

Back

Substituting x = -4 gives 5(-4) - y = -12, which simplifies to -20 - y = -12. Thus, y = -8, so the solution is (-4, -8).

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 - 7?

Back

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

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

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

Back

Setting y = 0 gives 0 = 2x - 7, which simplifies to x = 3.5, so the x-intercept is (3.5, 0).

Front

What does the term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The slope is 2.