what is the slope intercept equation witht the points (3,-5) and (-3,3)

To find the slope-intercept form of a line, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the two points \((3, -5)\) and \((-3, 3)\).

### Step 1: Calculate the slope \( m \)
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the points \((3, -5)\) and \((-3, 3)\):

\[
m = \frac{3 - (-5)}{-3 - 3} = \frac{3 + 5}{-6} = \frac{8}{-6} = -\frac{4}{3}
\]

### Step 2: Find the y-intercept \( b \)
Now that we know \( m = -\frac{4}{3} \), substitute one of the points into the slope-intercept form equation \( y = mx + b \) to solve for \( b \). We'll use the point \((3, -5)\):

\[
-5 = -\frac{4}{3}(3) + b
\]

Simplify:

\[
-5 = -4 + b
\]

Now, solve for \( b \):

\[
b = -5 + 4 = -1
\]

### Final equation:
Now we have the slope \( m = -\frac{4}{3} \) and the y-intercept \( b = -1 \). Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{4}{3}x - 1
\]

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:
1. How do you find the midpoint between two points?
2. What is the point-slope form of a line, and how does it compare to the slope-intercept form?
3. How can you graph a line given its slope and y-intercept?
4. What happens to the equation if the points are reversed?
5. How would you find the equation of a line perpendicular to this one?

**Tip:** When dealing with slopes, remember that a positive slope rises from left to right, while a negative slope falls.

what is the slope intercept equation with the points (3,-5) and (-3,3)

Discover how to find the slope-intercept form equation using the points (3, -5) and (-3, 3). This step-by-step guide demonstrates key algebraic concepts, including calculating the slope and finding the y-intercept. Suitable for students in Grades 8-10.

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