91Ó°ÊÓ

The slope-intercept form is an easy-to-use format for linear equations. It is expressed as \(y = mx + b\). In this equation:

• \(m\) represents the slope of the line, which shows how steep the line is.
• \(b\) is the y-intercept, the point where the line crosses the y-axis.

This form is popular because you can quickly identify both the slope and y-intercept by simply looking at the equation.
To find the y-intercept from a graph, locate the point where the line meets the y-axis. In the equation, check the value of \(b\); that’s the y-intercept.
To convert any linear equation into the slope-intercept form, you typically isolate \(y\) by rearranging the terms. Get the variable \(y\) on its own by using inverse operations such as addition, subtraction, multiplication, or division. Once \(y\) is alone, you'll have the equation in the form \(y = mx + b\).

The standard form of a linear equation is presented as \(Ax + By = C\). In this equation:

• \(A\), \(B\), and \(C\) are integers.
• \(A\) should be non-negative.
• It’s common to have \(A\), \(B\), and \(C\) keep a particular structure, like simplified form with no fractions.

The standard form is useful for analyzing certain algebraic aspects, like easily finding intercepts.
To find the y-intercept from a standard form equation, set \(x = 0\) and solve for \(y\). This gives you the point where the line meets the y-axis. To convert to slope-intercept form, solve the equation for \(y\) by manipulating it to arrange \(y\) by itself.

The point-slope form is used when you know a point on the line and the slope. It looks like this: \(y - y_1 = m(x - x_1)\). Here:

• \(m\) is the slope of the line.
• \((x_1, y_1)\) is a specific point on the line.

This form is particularly helpful when you do not have the y-intercept right away but know a point on the graph.
To find the y-intercept using this form, you can first solve for \(y\) to transform it into slope-intercept form (\(y = mx + b\)). This involves distributing \(m\) across \((x - x_1)\) and then adding \(y_1\) to both sides until you isolate \(y\).
Once in slope-intercept form, \(b\) will directly give you the y-intercept. By doing this conversion, you unlock a clearer view of your line’s behavior across the axes.