write the equation of the line in slope intercept form that passes through the point (-3,7) and (5,3)

To find the equation of the line in slope-intercept form \( y = mx + b \) that passes through the points \((-3, 7)\) and \((5, 3)\), follow these steps:

### Step 1: Find the slope \( m \) of the line.
The slope \( m \) is given by the formula:

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

Substituting the given points \((-3, 7)\) and \((5, 3)\):

\[
m = \frac{3 - 7}{5 - (-3)} = \frac{-4}{8} = -\frac{1}{2}
\]

### Step 2: Use the point-slope form of the equation.
Now, use the point-slope form of the line equation:

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

Using the slope \( m = -\frac{1}{2} \) and one of the points, say \((-3, 7)\):

\[
y - 7 = -\frac{1}{2}(x + 3)
\]

### Step 3: Simplify to get the slope-intercept form.
Distribute and simplify the equation:

\[
y - 7 = -\frac{1}{2}x - \frac{3}{2}
\]

Add 7 to both sides to solve for \( y \):

\[
y = -\frac{1}{2}x - \frac{3}{2} + \frac{14}{2}
\]

\[
y = -\frac{1}{2}x + \frac{11}{2}
\]

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

\[
\boxed{y = -\frac{1}{2}x + \frac{11}{2}}
\]

Would you like further details or have any questions?

Here are some related questions you might find useful:
1. How do you find the slope-intercept form given two points?
2. How do you convert a point-slope equation to slope-intercept form?
3. What is the significance of the slope in a linear equation?
4. How do you determine if two lines are parallel?
5. How can you find the y-intercept if the equation is given in standard form?

**Tip:** The slope-intercept form \( y = mx + b \) is useful for quickly identifying the slope \( m \) and the y-intercept \( b \) of a line.

Learn how to write the equation of a line in slope-intercept form that passes through the points (-3,7) and (5,3). This detailed solution explains key algebraic concepts, including the slope formula and the point-slope form, suitable for students in Grades 8-10.

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