To write the equation of this line in slope-intercept form $y = mx + b$, let’s determine the slope ($m$) and the y-intercept ($b$).

Step 1: Find the Slope ($m$)

The slope formula is: $m = \frac{\text{rise}}{\text{run}}$ From the graph, we can select two points on the line:

• Point 1: $(-40, -40)$
• Point 2: $(0, 10)$

Using these points: $m = \frac{10 - (-40)}{0 - (-40)} = \frac{10 + 40}{40} = \frac{50}{40} = \frac{5}{4}$

Step 2: Identify the y-Intercept ($b$)

The line crosses the y-axis at $y = 10$, so the y-intercept $b = 10$.

Step 3: Write the Equation

Now, substitute $m = \frac{5}{4}$ and $b = 10$ into the slope-intercept form: $y = \frac{5}{4}x + 10$

Final Answer

The equation of the line is: $y = \frac{5}{4}x + 10$

Would you like more details on how to calculate slope or y-intercepts?

Related Questions:

1. How do you find the equation of a line given two points?
2. What are other forms to express a line’s equation besides slope-intercept form?
3. How do changes in slope affect the steepness of a line?
4. What does the y-intercept tell us about a line?
5. How would you convert a slope-intercept equation to standard form?

Tip: When identifying the slope, always pick points that align exactly with the grid for accuracy.