91Ó°ÊÓ

The x-intercept is where a line crosses the x-axis. This point has a y-coordinate of 0 because it lies on the x-axis. In our exercise, the x-intercept is given as 1. This means that the line crosses the x-axis at the point (1, 0).

To find the x-intercept from an equation, you set y to 0 and solve for x.
For example, if you have the equation of a line as \(3x - y = 3\), set \(y = 0\):

\[ 3x - 0 = 3 \ x = 1 \]

This confirms our x-intercept point (1, 0).

The y-intercept is where a line crosses the y-axis. This point has an x-coordinate of 0 because it lies on the y-axis. In our exercise, the y-intercept is given as -3. This means the line crosses the y-axis at the point (0, -3).

To find the y-intercept from an equation, you set x to 0 and solve for y.
For example, if you have the equation of a line as \(3x - y = 3\), set \(x = 0\):

\[ 3(0) - y = 3 \ -y = 3 \ y = -3 \]

This confirms our y-intercept point (0, -3).

The equation of a line can be represented in several forms. In this exercise, we are using the intercept form of the line equation.

The intercept form is \(\frac{x}{a} + \frac{y}{b} = 1\) where \(a\) is the x-intercept and \(b\) is the y-intercept. Substituting the intercepts 1 and -3 into the equation, we get:

\[ \frac{x}{1} + \frac{y}{-3} = 1 \]

Simplifying, we get:

\[ x - \frac{y}{3} = 1 \]

To further simplify into the standard form \(Ax + By = C\), we multiply through by 3:

\[ 3x - y = 3 \]

This is the final equation of the given line.

Understanding the different forms of line equations and how to convert between them is crucial for solving many algebra problems.