Question

Write an equation in slope intervept form for the line that passes through (5,-6) and is parraklel to the line described by y=-x+3.

Answer 1

No we need to use slope intervept form, not point slope form

Answer 2

To find the equation of a line that passes through the point (5, -6) and is parallel to the line given by the equation \(y = -x + 3\), we need to determine the slope of the given line.

The equation \(y = -x + 3\) is in slope-intercept form, where the slope \(m\) is the coefficient of \(x\). In this case, the slope is \(-1\).

Since parallel lines have the same slope, the slope of the line we are looking for is also \(-1\).

Now we can use the point-slope form of a linear equation, which is given by:

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

Here, \((x_1, y_1)\) is the point (5, -6) and \(m = -1\). Plugging in these values:

\[
y - (-6) = -1(x - 5)
\]

This simplifies to:

\[
y + 6 = -1(x - 5)
\]

Now distribute \(-1\):

\[
y + 6 = -x + 5
\]

Next, we subtract 6 from both sides:

\[
y = -x + 5 - 6
\]

\[
y = -x - 1
\]

Thus, the equation of the line in slope-intercept form is:

\[
\boxed{y = -x - 1}
\]

Answer 3

Apologies for any confusion. Let's derive the equation directly in slope-intercept form (which is \(y = mx + b\)) using the information provided.

We have already established the slope of the parallel line as \(-1\). Now, we need to find the y-intercept \(b\) using the point (5, -6).

We can start with the slope-intercept form:

\[
y = mx + b
\]

Substituting in the slope:

\[
y = -x + b
\]

Now, we can plug in the coordinates of the point (5, -6) to find \(b\):

\[
-6 = -1(5) + b
\]

This simplifies to:

\[
-6 = -5 + b
\]

Now, solve for \(b\):

\[
-6 + 5 = b
\]

\[
b = -1
\]

Now, we have the slope and y-intercept, so we can write the slope-intercept form of the equation:

\[
\boxed{y = -x - 1}
\]

This is the equation of the line that passes through the point (5, -6) and is parallel to the line described by \(y = -x + 3\).