Answer:[tex]\begin{gathered} \text{Slope = }\frac{1}{2} \\ y\text{ +2= }\frac{1}{2}(x\text{ + 9) (point-slope form)} \\ y\text{ = }\frac{1}{2}x\text{ + }\frac{5}{2}(\text{slope}-\text{intercept form)} \end{gathered}[/tex]Explanations:
The slope, m, of a line passing therough the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
For the points (-9, -2) and (1, 3):
x₁ = -9, y₁ = -2, x₂ = 1, y₂ = 3
Substituting these points into the slope formula given above
[tex]\begin{gathered} m\text{ = }\frac{3-(-2)}{1-(-9)} \\ m\text{ = }\frac{5}{10} \\ m\text{ = }\frac{1}{2} \end{gathered}[/tex]
The slope, m = 1/2
The point-slope form of the equation of a line passing through the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - (-2) = }\frac{1}{2}(x\text{ - (-9))} \\ y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \end{gathered}[/tex]
The slope-intercept form of the equation will be of the form y = mx + c
Reduce the point-slope form written above to the intercept-slope form
[tex]\begin{gathered} y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \\ y\text{ + 2 = }\frac{x}{2}+\text{ }\frac{9}{2} \\ y\text{ = }\frac{x}{2}+\frac{9}{2}-2 \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{5}{2} \end{gathered}[/tex]
