Question

Use the following two points to answer parts a - c. (10, 2), (2, - 2) a . Find the slope of the line passing through the two points. b . Write an equation of a line passing through the two points in point-slope form. c . Rewrite the equation of the line in slope-intercept form.

Answer 1

a) 0.5

b) y - = 0.5(x - 10)

c) y = 0.5x - 3

Step-by-step explanation

We are given the points (10, 2) and (2, -2)

a) Slope is given as the rate of change of y with respect to the change of x.

To find the slope, we use the formula:

`\text{slope = }\frac{y_2-y_{1_{}_{}}}{x_2-x_1}`

where (x1, y1) = (10, 2) and (x2, y2) = (2, -2)

So, the slope is:

`\begin{gathered} \text{slope = }\frac{-2\text{ -2}}{2\text{ - 10}}\text{ = }(-4)/(-8) \\ \text{slope = 0.5} \end{gathered}`

b) To write an equation in point-slope form, we have to write the equation in the form:

`y-y_1=m(x_{}-x_1)`

where m = slope

So, we have that in point slope form:

y - 2 = 0.5(x - 10)

c) To write the equation in slope-intercept form, we have to write it in the form:

y = mx + c

To do that we have to simplify the point-slope form of the equation.

We have:

y - 2 = 0.5(x - 10)

Expand the bracket:

y - 2 = 0.5x - 5

Collect like terms:

y = 0.5x - 5 + 2

y = 0.5x - 3