Question: Write the equation of this line in slope-intercept form.
The graph shows a straight line with arrows on both ends, rising from bottom-left to top-right, crossing the y-axis at 1 and passing through points such as (4, 4) and (8, 7); position_hint: center.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
1. **State the problem:** We need to find the equation of the line in slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept.
2. **Identify given points and y-intercept:** The line crosses the y-axis at $$b = 1$$, and passes through points $$(4, 4)$$ and $$(8, 7)$$.
3. **Calculate the slope $$m$$:**
$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 4}{8 - 4} = \frac{3}{4}$$
4. **Write the slope-intercept form:**
Since $$b = 1$$ and $$m = \frac{3}{4}$$, the equation is:
$$y = \frac{3}{4}x + 1$$
5. **Verify with a point:**
Using point $$(4,4)$$:
$$y = \frac{3}{4} \times 4 + 1 = 3 + 1 = 4$$ which matches the point.
**Final answer:**
$$y = \frac{3}{4}x + 1$$