Question

write an equation of a line passing through the points (-5,6) and (5,2)

Answer 1

write an equation of a line passing through the points (-5,6) and (5,2) in slope intercept form

Answer 2

To find the equation of the line passing through the points \((-5, 6)\) and \((5, 2)\), we first need to determine the slope (m) of the line. The slope can be calculated using the formula:

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

For the points \((-5, 6)\) (where \(x_1 = -5\) and \(y_1 = 6\)) and \((5, 2)\) (where \(x_2 = 5\) and \(y_2 = 2\)), we can substitute these coordinates into the formula:

\[
m = \frac{2 - 6}{5 - (-5)} = \frac{2 - 6}{5 + 5} = \frac{-4}{10} = -\frac{2}{5}
\]

Now that we have the slope \(m = -\frac{2}{5}\), we can use the point-slope form of the equation of a line, which is:

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

We can use either of the two points; let's use \((-5, 6)\):

\[
y - 6 = -\frac{2}{5}(x - (-5))
\]

This simplifies to:

\[
y - 6 = -\frac{2}{5}(x + 5)
\]

Now, distribute the slope:

\[
y - 6 = -\frac{2}{5}x - 2
\]

Now, add 6 to both sides:

\[
y = -\frac{2}{5}x - 2 + 6
\]

This simplifies to:

\[
y = -\frac{2}{5}x + 4
\]

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

\[
\boxed{y = -\frac{2}{5}x + 4}
\]

Answer 3

To find the equation of the line that passes through the points \((-5, 6)\) and \((5, 2)\) in slope-intercept form (\(y = mx + b\)), we first need to determine the slope \(m\) using the formula:

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

For the points \((-5, 6)\) (where \(x_1 = -5\) and \(y_1 = 6\)) and \((5, 2)\) (where \(x_2 = 5\) and \(y_2 = 2\)), we substitute into the formula:

\[
m = \frac{2 - 6}{5 - (-5)} = \frac{2 - 6}{5 + 5} = \frac{-4}{10} = -\frac{2}{5}
\]

Now that we have the slope \(m = -\frac{2}{5}\), we can use the slope-intercept form, which is \(y = mx + b\). To find \(b\), the y-intercept, we can substitute one of the points into the equation. Let's use the point \((-5, 6)\):

\[
6 = -\frac{2}{5}(-5) + b
\]

Calculating \(-\frac{2}{5}(-5)\):

\[
6 = 2 + b
\]

Next, we solve for \(b\):

\[
b = 6 - 2 = 4
\]

Now we can write the equation of the line in slope-intercept form:

\[
y = -\frac{2}{5}x + 4
\]

Thus, the equation of the line passing through the points \((-5, 6)\) and \((5, 2)\) is:

\[
\boxed{y = -\frac{2}{5}x + 4}
\]