Intermediate Algebra/Linear Equations

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Linear Equations[edit]

A linear equation is an equation that forms a line on a graph.

Slope-Intercept form[edit]

A linear equation in slope-intercept form is one in the form such that is the slope, and is the y-intercept. An example of such an equation is:

Finding y-intercept, given slope and a point[edit]

The y-intercept of an equation is the point at which the line produced touches the y-axis, or the point where This can be very useful. If we know the slope, and a point which the line passes through, we can find the y-intercept. Consider:

Which passes through
Substitute and for and , respectively
Simplify.

Put into slope-intercept form.

Finding slope, given y-intercept and a point[edit]

The slope of a line is defined as the amount of change in x and y between two points on the line.

If we know the y-intercept of the line, and a point on the line, we can easily find the slope. Consider:

which passes through the point

Replace and with and , respectively. Simplify. Put into slope-intercept form.


Standard form[edit]

The Standard form of a line is the form of a linear equation in the form of such that and are integers, and .

Converting from slope-intercept form to standard form[edit]

Slope-intercept equations can easily be changed to standard form. Consider the equation:

Subtract -3x from each side, satisfying
Multiply the entire equation by , satisfying
and are already integers, so we don't have to worry about changing them.

Finding the slope of an equation in standard form[edit]

In the standard form of an equation, the slope is always equal to