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 = }(1)/(2) \\ y\text{ +2= }(1)/(2)(x\text{ + 9) (point-slope form)} \\ y\text{ = }(1)/(2)x\text{ + }(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{ = }(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{ = }(3-(-2))/(1-(-9)) \\ m\text{ = }(5)/(10) \\ m\text{ = }(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) = }(1)/(2)(x\text{ - (-9))} \\ y\text{ + 2 = }(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 = }(1)/(2)(x\text{ + 9)} \\ y\text{ + 2 = }(x)/(2)+\text{ }(9)/(2) \\ y\text{ = }(x)/(2)+(9)/(2)-2 \\ y\text{ = }(1)/(2)x\text{ +}(5)/(2) \end{gathered}`