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A line on a coordinate plane passes through the point 2 comma negative 7 and has a slope of 0.75.

Question
When the line passes through x equals negative 6, what is the value of y? Enter the answer in the box.

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Answer 1

To find the value of \( y \) when \( x = -6 \) for a line that passes through the point \( (2, -7) \) with a slope of \( 0.75 \), we can use the point-slope form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) \) is the point the line passes through, and \( m \) is the slope.

Here, \( (x_1, y_1) = (2, -7) \) and \( m = 0.75 \).

Substituting these values into the equation:

\[
y - (-7) = 0.75(x - 2)
\]

Simplifying it:

\[
y + 7 = 0.75(x - 2)
\]
\[
y + 7 = 0.75x - 1.5
\]
\[
y = 0.75x - 1.5 - 7
\]
\[
y = 0.75x - 8.5
\]

Now we will substitute \( x = -6 \) into the equation:

\[
y = 0.75(-6) - 8.5
\]
\[
y = -4.5 - 8.5
\]
\[
y = -13
\]

Thus, when the line passes through \( x = -6 \), the value of \( y \) is \( \boxed{-13} \).