Question

Example(-9, -2) (1,3)Find the slopeWrite in point slopeWrite in slope intercept formComplete the same three steps for 50extra points using the points(-6,7)(-3,6)

Answer 1

Answer:$\begin{gathered} \text{Slope = }\frac{1}{2} \\ y\text{ +2= }\frac{1}{2}(x\text{ + 9) (point-slope form)} \\ y\text{ = }\frac{1}{2}x\text{ + }\frac{5}{2}(\text{slope}-\text{intercept form)} \end{gathered}$Explanations:

The slope, m, of a line passing therough the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

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

$\begin{gathered} m\text{ = }\frac{3-(-2)}{1-(-9)} \\ m\text{ = }\frac{5}{10} \\ m\text{ = }\frac{1}{2} \end{gathered}$

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

$\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - (-2) = }\frac{1}{2}(x\text{ - (-9))} \\ y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \end{gathered}$

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

$\begin{gathered} y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \\ y\text{ + 2 = }\frac{x}{2}+\text{ }\frac{9}{2} \\ y\text{ = }\frac{x}{2}+\frac{9}{2}-2 \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{5}{2} \end{gathered}$