Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.

(2,−5)
  (0,−2)

To find the equation of a line in slope-intercept form (\(y = mx + b\)), we need two pieces of information:
1. The slope (\(m\))
2. The y-intercept (\(b\))

### Step 1: Find the slope \(m\)
The slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

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

Here, the two points are:
\[
(2, -5) \quad \text{and} \quad (0, -2)
\]

Substitute the values into the slope formula:
\[
m = \frac{-2 - (-5)}{0 - 2} = \frac{-2 + 5}{-2} = \frac{3}{-2} = -\frac{3}{2}
\]

### Step 2: Use the slope-intercept form \(y = mx + b\)
Now that we have the slope, \(m = -\frac{3}{2}\), we can substitute it into the slope-intercept form:
\[
y = -\frac{3}{2}x + b
\]

### Step 3: Find the y-intercept \(b\)
To find \(b\), we can use one of the given points. Let's use the point \((0, -2)\), where \(x = 0\) and \(y = -2\). Plug these values into the equation \(y = -\frac{3}{2}x + b\):

\[
-2 = -\frac{3}{2}(0) + b
\]

Simplifying:
\[
-2 = b
\]

So, the y-intercept is \(b = -2\).

### Final equation:
Now, substitute \(b = -2\) and \(m = -\frac{3}{2}\) into the slope-intercept form:

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

This is the equation of the line.

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Would you like further details on any step? Here are some related questions for practice:

1. Find the equation of a line passing through points \((3, 4)\) and \((6, 7)\).
2. What is the slope of a line parallel to the line \(y = \frac{5}{3}x + 1\)?
3. Determine the equation of a line with slope \(2\) and passing through the point \((1, -3)\).
4. How do you find the equation of a line given its slope and one point?
5. Find the slope of a line passing through \((4, 8)\) and \((7, 14)\).

**Tip:** The slope of a line remains the same for all points along that line. This makes the slope a very useful property for determining equations of lines.

Find the equation (in slope-intercept form) of the line passing through the points (2, -5) and (0, -2).

Learn how to find the equation of a line in slope-intercept form passing through the points (2, -5) and (0, -2). This problem involves using the slope formula and determining the y-intercept, making it suitable for students in Grades 8-10.

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