Question: 7. y = 2/3 x + 10
1. **State the problem:** We are given the linear equation $$y = \frac{2}{3}x + 10$$ and we want to understand its properties and graph it.
2. **Formula and explanation:** This is a linear equation in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept.
3. **Identify slope and intercept:** Here, the slope $$m = \frac{2}{3}$$ and the y-intercept $$b = 10$$.
4. **Interpret slope:** The slope $$\frac{2}{3}$$ means for every increase of 3 units in $$x$$, $$y$$ increases by 2 units.
5. **Plot intercept:** The line crosses the y-axis at $$y = 10$$ when $$x = 0$$.
6. **Find x-intercept:** Set $$y=0$$ to find x-intercept:
$$0 = \frac{2}{3}x + 10$$
$$\Rightarrow \frac{2}{3}x = -10$$
$$\Rightarrow x = -10 \times \frac{3}{2}$$
$$\Rightarrow x = -15$$
7. **Summary:** The line passes through points $$(0,10)$$ and $$(-15,0)$$ with slope $$\frac{2}{3}$$.
This completes the analysis of the linear equation.