write the equation of the line in slope intercept form through (-4,5) and (-3-2)



To write the equation of a line in **slope-intercept form** (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

### Step 1: Find the slope (\(m\))
The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (-4, 5) \) and \( (-3, -2) \):
\[
m = \frac{-2 - 5}{-3 - (-4)} = \frac{-7}{-3 + 4} = \frac{-7}{1} = -7
\]
So, the slope \( m = -7 \).

### Step 2: Use the point-slope form to find the equation
The point-slope form of the equation is:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = -7 \) and using the point \( (-4, 5) \):
\[
y - 5 = -7(x - (-4)) = -7(x + 4)
\]

### Step 3: Simplify to slope-intercept form (\( y = mx + b \))
Now, simplify the equation:
\[
y - 5 = -7(x + 4)
\]
Distribute the \( -7 \):
\[
y - 5 = -7x - 28
\]
Add 5 to both sides:
\[
y = -7x - 23
\]

So, the equation of the line is:
\[
y = -7x - 23
\]

Let me know if you'd like any more details on the solution!

Here are 5 related questions you can explore:
1. What is the y-intercept of the line?
2. How do you find the equation of a line perpendicular to this one through a given point?
3. What is the general form of a linear equation, and how is it related to slope-intercept form?
4. Can you verify the line equation by substituting the second point?
5. What happens to the slope if the two points are swapped?

**Tip**: Always double-check calculations when finding the slope, as it's key to determining the correct line equation.

write the equation of the line in slope intercept form through (-4,5) and (-3-2)

Learn how to find the equation of a line passing through points (-4, 5) and (-3, -2) in slope-intercept form. This guide covers essential algebraic concepts such as calculating the slope and applying the slope-intercept equation y = mx + b. Perfect for students in Grades 8-10.

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