Each table of values gives several points that lie on a...

Each table of values gives several points that lie on a line. (a) What is the x-intercept of the line? The y-intercept? (b) Which equation in choices $A-D$ corresponds to the given table of values? (c) Graph the equation. $$\begin{array}{c|c}x & y \\\hline-2 & -1 \\\hline 0 & -1 \\\hline 2 & -1 \\\hline 4 &-1\end{array}$$ A. $y=-1$ B. $y=1$ C. $x=1$ D. $x=-1$

Each table of values gives several points that lie on a line.
(a) What is the x-intercept of the line? The y-intercept?
(b) Which equation in choices $A-D$ corresponds to the given table of values?
(c) Graph the equation.
$$\begin{array}{c|c}x & y \\\hline-2 & -1 \\\hline 0 & -1 \\\hline 2 & -1 \\\hline 4 &-1\end{array}$$
A. $y=-1$
B. $y=1$
C. $x=1$
D. $x=-1$

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Key Concepts

Intercepts

Intercepts are the points where a line crosses the axes. The x-intercept is where the line meets the x-axis (where y = 0), and the y-intercept is where it meets the y-axis (where x = 0). Understanding intercepts is crucial since they provide key information about the position of a line in the coordinate plane.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form not only makes it easy to identify the y-intercept directly from the equation but also shows how the line rises or falls as x increases.

Horizontal Lines

A horizontal line is characterized by a constant y-value across all x-values, which means its slope is 0. Horizontal lines have the form y = c, where c is the constant y-value. Recognizing horizontal lines helps in understanding that such lines have no x-intercept when c is not 0, or have special graphical characteristics.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation and drawing the line that passes through these points. It requires identification of key features such as intercepts, slope, and any patterns in a table of values. This skill is fundamental in visualizing and analyzing linear relationships.

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