The equation of the line passing through the points (0,-3),(1,-1) in slope-intercept form  is

To find the equation of the line passing through the points \((0, -3)\) and \((1, -1)\) in slope-intercept form \(y = mx + b\), we follow these steps:

1. **Calculate the slope (\(m\))**:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-3)}{1 - 0} = \frac{-1 + 3}{1} = \frac{2}{1} = 2
   \]

2. **Use the slope-intercept form**:
   Since we know the slope \(m = 2\), the equation starts as:
   \[
   y = 2x + b
   \]

3. **Find the \(y\)-intercept (\(b\))**:
   Use one of the given points, for example, \((0, -3)\):
   \[
   -3 = 2(0) + b \implies b = -3
   \]

4. **Write the final equation**:
   \[
   y = 2x - 3
   \]

So, the equation of the line in slope-intercept form is \(y = 2x - 3\).

Would you like more details on this process or have any questions?

Here are 8 related questions you might find helpful:
1. How do you find the slope if the points are \((2, 5)\) and \((4, 9)\)?
2. What is the point-slope form of the equation for the same line?
3. How do you find the equation of a line given its slope and a point on the line?
4. Can you find the equation of a line parallel to \(y = 2x - 3\) that passes through the point \((2, 4)\)?
5. What is the slope of a line perpendicular to \(y = 2x - 3\)?
6. How do you convert a slope-intercept equation to standard form?
7. What does the slope represent in the context of a real-world problem?
8. How do you graph the equation \(y = 2x - 3\) on a coordinate plane?

**Tip:** Always double-check your slope calculations, as a small error can lead to the wrong equation of the line!

Learn how to find the equation of a line passing through the points (0, -3) and (1, -1) using the slope-intercept form. Detailed step-by-step solution provided.

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