Linear Equations - Find Solutions

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 the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

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

Back

A point (x, y) is a solution to a linear equation if, when you substitute x into the equation, the resulting value of y is equal to the y-coordinate of the point.

Front

What does it mean for points to be 'on' a line in the context of linear equations?

Back

Points that are 'on' the line are solutions to the linear equation, meaning they satisfy the equation when their coordinates are substituted into it.

Front

What is the significance of the equation y = 5x?

Back

The equation y = 5x represents a linear relationship where the slope is 5, indicating that for every 1 unit increase in x, y increases by 5 units.

Front

If (1, 5) is a solution to the equation y = 5x, what does this mean?

Back

It means that when x = 1, substituting it into the equation gives y = 5, confirming that the point (1, 5) lies on the line represented by the equation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How can you find the equation of a line given two points?

Back

To find the equation of a line given two points, calculate the slope using the formula (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to write the equation.

Front

What does it mean for a linear equation to have no solution?

Back

A linear equation has no solution if the lines represented by the equations are parallel and never intersect.