In Exercises 105-108, use the results of Exercises 101-104...

In Exercises 105-108, use the results of Exercises 101-104 to write an equation of the line that passes through the points.
$\begin{aligned} & x \text {-intercept: }\left(-\frac{1}{6}, 0\right) \\ & y \text {-intercept: }\left(0,-\frac{2}{3}\right)\end{aligned}$

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Key Concepts

Intercepts

Intercepts are the points where a line crosses the coordinate axes. The x-intercept is where the line crosses the x-axis (y = 0) and the y-intercept is where it crosses the y-axis (x = 0). These points are essential for plotting lines and for deriving linear equations.

Slope

The slope of a line measures its steepness and direction. It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. Knowing the slope allows one to understand how rapidly the line rises or falls.

Point-Slope Form

The point-slope form is a way to express the equation of a line using its slope and a specific point on the line. It is written as y - y? = m(x - x?), where m is the slope and (x?, y?) is a point through which the line passes.

Slope-Intercept Form

The slope-intercept form of a linear equation, given by y = mx + b, directly shows the slope (m) and the y-intercept (b) of the line. This form is particularly useful for graphing lines, as it immediately reveals how the line interacts with the y-axis.

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