find an equation for the line with the given properties express your answer using either the general form or the slop intercept form of the equation of a line slope=-3 containing point 3,-5

To find the equation of the line with a slope of \(-3\) and passing through the point \((3, -5)\), we can use the point-slope form of a line equation:

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

Where:
- \(m\) is the slope,
- \((x_1, y_1)\) is a point on the line.

Substitute the given values:
- Slope \(m = -3\),
- Point \((x_1, y_1) = (3, -5)\).

\[
y - (-5) = -3(x - 3)
\]

Simplify the equation:

\[
y + 5 = -3(x - 3)
\]

Now expand and solve for \(y\):

\[
y + 5 = -3x + 9
\]
\[
y = -3x + 9 - 5
\]
\[
y = -3x + 4
\]

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

\[
y = -3x + 4
\]

If you prefer the general form \(Ax + By + C = 0\), rearrange the equation:

\[
3x + y - 4 = 0
\]

Thus, the equation of the line in general form is:

\[
3x + y - 4 = 0
\]

Would you like more details or clarifications?

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Here are 5 related questions to explore:
1. How do you convert from slope-intercept form to point-slope form?
2. What is the relationship between the slope and parallel lines?
3. How do you find the equation of a line given two points?
4. How can you determine if a point lies on a given line?
5. How do you calculate the slope of a perpendicular line?

**Tip**: Always simplify equations as much as possible to avoid errors when using them in further calculations.

find an equation for the line with the given properties express your answer using either the general form or the slope-intercept form of the equation of a line slope=-3 containing point 3,-5

Learn how to find the equation of a line with a slope of -3 passing through the point (3, -5). This problem explores linear equations, using both the slope-intercept and point-slope forms. Detailed step-by-step solution provided. Suitable for students in Grades 8-10.

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