Write the slope-intercept form, y=mx+b for the following linear relationship.
a line that passes through the points (0, -10) and (5, 0)

To find the slope-intercept form of the equation \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

1. **Find the slope \( m \):**

   The slope \( m \) is calculated using the formula:

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

   For the points \((0, -10)\) and \((5, 0)\):

   \[
   m = \frac{0 - (-10)}{5 - 0} = \frac{10}{5} = 2
   \]

   So, the slope \( m \) is 2.

2. **Find the y-intercept \( b \):**

   Since the line passes through the point \((0, -10)\), this is the y-intercept. Therefore, \( b = -10 \).

3. **Write the equation:**

   Substitute the values of \( m \) and \( b \) into the slope-intercept form:

   \[
   y = 2x - 10
   \]

So, the equation of the line in slope-intercept form is \( y = 2x - 10 \).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you find the slope of a line if given two points?
2. What is the significance of the y-intercept in a linear equation?
3. How do you graph a line given its slope-intercept form?
4. What are parallel and perpendicular lines in terms of their slopes?
5. How can you convert a linear equation from standard form to slope-intercept form?

**Tip:** Always check your calculations by substituting the points back into the final equation to ensure they satisfy the equation.

Learn how to find the slope-intercept form y=mx+b for a line passing through points (0, -10) and (5, 0). This problem covers key concepts in linear equations, including the slope formula and slope-intercept form. Suitable for students in Grades 7-9.

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