Sketch the lines through the given point with the indicated...

Sketch the lines through the given point with the indicated slopes. Make the sketches on the same set of coordinate axes. $$ \begin{array}{llllll} \text { 3. } \frac{\text { Point }}{(2,3)} & \text { Slopes } & \\ \hline \text { a) } 1 & \text { (b) }-2 & \text { (c) }-\frac{3}{2} & \text { (d) Undefined } \end{array} $$

Sketch the lines through the given point with the indicated slopes. Make the sketches on the same set of coordinate axes.
$$
\begin{array}{llllll}
\text { 3. } \frac{\text { Point }}{(2,3)} & \text { Slopes } & \\
\hline \text { a) } 1 & \text { (b) }-2 & \text { (c) }-\frac{3}{2} & \text { (d) Undefined }
\end{array}
$$

Key Concepts

Slope

The slope of a line is a measure of its steepness and direction, calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run). It indicates how much the line rises or falls for each unit of horizontal movement and is fundamental in understanding linear relationships.

Point-Slope Form

The point-slope form is an equation of a line that uses a known point and a given slope. It is expressed as y - y? = m(x - x?), where (x?, y?) is a specific point on the line and m is the slope. This form is particularly useful when you know one point on the line and the line’s slope.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope and b represents the y-intercept, the point where the line crosses the y-axis. It is a convenient form for graphing linear equations and understanding the line's behavior in the coordinate plane.

Graphing Linear Equations

Graphing linear equations involves plotting the line on a coordinate system by identifying key components such as the slope and the y-intercept, or by using a specific point and the slope. After determining these elements, additional points can be found following the slope, and then these points are connected to draw the line.

Vertical Lines

A vertical line is one that runs up and down the coordinate plane and is characterized by an undefined slope because the change in x is zero. Vertical lines are represented by equations of the form x = c, where c is a constant value, indicating that all points on the line share the same x-coordinate.

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