1. **State the problem:** We are given two points on a line: $(-5,-4)$ and $(5,3)$. We need to find the equation of the line passing through these points and analyze its properties. 2. **Find the slope ($m$):** The slope formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ Substitute the points: $$m=\frac{3 - (-4)}{5 - (-5)}=\frac{3 + 4}{5 + 5}=\frac{7}{10}$$ 3. **Find the equation of the line:** Use point-slope form: $$y - y_1 = m(x - x_1)$$ Using point $(-5,-4)$: $$y - (-4) = \frac{7}{10}(x - (-5))$$ $$y + 4 = \frac{7}{10}(x + 5)$$ 4. **Simplify to slope-intercept form ($y=mx+b$):** $$y = \frac{7}{10}x + \frac{7}{10} \times 5 - 4$$ $$y = \frac{7}{10}x + \frac{35}{10} - 4$$ $$y = \frac{7}{10}x + 3.5 - 4$$ $$y = \frac{7}{10}x - 0.5$$ 5. **Analyze properties:** - Degree: 1 (linear function) - Shape: straight line - Leading coefficient (slope): $\frac{7}{10}$ - Number of x-intercepts: 1 - Find x-intercept by setting $y=0$: $$0 = \frac{7}{10}x - 0.5$$ $$\frac{7}{10}x = 0.5$$ $$x = \frac{0.5}{\frac{7}{10}} = 0.5 \times \frac{10}{7} = \frac{5}{7}$$ - x-intercept: $\left(\frac{5}{7}, 0\right)$ - y-intercept: set $x=0$: $$y = \frac{7}{10} \times 0 - 0.5 = -0.5$$ - y-intercept: $(0, -0.5)$ - End behavior: as $x \to \infty$, $y \to \infty$; as $x \to -\infty$, $y \to -\infty$ - Domain: all real numbers - Range: all real numbers - Number of turning points: 0 (linear function has no turning points)