Question

Which is the equation of the line shown in the graph? (1 point)
A line is drawn through -6, -6 and 2, 5

Responses y=118x+94 y is equal to 11 eighths x plus 9 fourths y=94x+118 y is equal to 9 fourths x plus 11 eighths y=118x+2 y is equal to 11 eighths x plus 2 y=13x+133 y is equal to 1 third x plus 13 thirds Skip to navigation

Answer 1

To find the equation of the line that passes through the points \((-6, -6)\) and \((2, 5)\), we first need to calculate the slope \(m\) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the coordinates \( (x_1, y_1) = (-6, -6) \) and \( (x_2, y_2) = (2, 5) \):

\[
m = \frac{5 - (-6)}{2 - (-6)} = \frac{5 + 6}{2 + 6} = \frac{11}{8}
\]

Next, we can use the point-slope form of the line equation \(y - y_1 = m(x - x_1)\). Using point \((-6, -6)\):

\[
y - (-6) = \frac{11}{8}(x - (-6))
\]
\[
y + 6 = \frac{11}{8}(x + 6)
\]
\[
y + 6 = \frac{11}{8}x + \frac{11}{8} \times 6
\]
\[
y + 6 = \frac{11}{8}x + \frac{66}{8}
\]
\[
y = \frac{11}{8}x + \frac{66}{8} - 6
\]
\[
y = \frac{11}{8}x + \frac{66}{8} - \frac{48}{8}
\]
\[
y = \frac{11}{8}x + \frac{18}{8}
\]
\[
y = \frac{11}{8}x + \frac{9}{4}
\]

Thus, the equation of the line is:

\[
y = \frac{11}{8}x + \frac{9}{4}
\]

Looking at the provided responses, the answer is:

**y = 9/4 x + 11/8**.