Question

write the equation of a line that passes through the points shown in the table.

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline -10 & 2 \\\\ \\hline -4 & 1 \\\\ \\hline 8 & -1 \\\\ \\hline 14 & -2 \\\\ \\hline \\end{array}$$

which equations represent a line that passes through the points given in the table? check all that apply.

\\(y - 2 = -6(x + 10)\\)
\\(y - 2 = -\frac{1}{6}(x + 10)\\)
\\(y - 1 = -\frac{1}{6}(x + 4)\\)
\\(y = -6x - 58\\)
\\(y = -\frac{1}{6}x + \frac{1}{3}\\)
\\(y = -\frac{1}{6}x + 5\\)

Explanation:

Calculate the slope of the line

Using the Slope Formula knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 2}{-4 - (-10)} = \frac{-1}{6} = -\frac{1}{6} $$

Write equations in point-slope form

Using the Point-Slope Form knowledge point

$$
LATEXBLOCK0
$$

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Evaluate the given options

Using the Slope-Intercept Form and Point-Slope Form knowledge points

$$
LATEXBLOCK2
$$

Answer:

• \(y - 2 = -6(x + 10)\)
• \(y - 2 = -\frac{1}{6}(x + 10)\) (Correct answer)
• \(y - 1 = -\frac{1}{6}(x + 4)\) (Correct answer)
• \(y = -6x - 58\)
• \(y = -\frac{1}{6}x + \frac{1}{3}\) (Correct answer)
• \(y = -\frac{1}{6}x + 5\)