Question

#4 What is the equation of the line that passes through the points (3, 6) and (8, 14) ? Write the equation in point-slope form and slope-intercept form.

Answer 1

slope-intercept form: y = 8x/5 + 1.2 or y = 1.6x + 1.2

point-slope form: y - 6 = 8/5(x - 3) or y - 6 = 1.6(x -3)

Step-by-step explanation:

Given points (3, 6) and (8, 14) = (x1, y1) and (x2, y2)

We use the linear equation:

y = mx + c

m = slope and c = intercept

The slope formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} m\text{ =}(14-6)/(8-3)\text{ = }(8)/(5) \\ m\text{ = 8/5} \end{gathered}`

We use any of the points given to find the intercept

using point (3, 6) , we insert in our linear equation:

6 = 8/5 (3) + c

6 = 24/5 + c

c = 6 - 24/5 = 6 - 4.8

c = 1.2

The linear equation becomes:

y = 8/5 (x) + 1.2

The slope intercept form: y = 8x/5 + 1.2 or y = 1.6x + 1.2

Point slope form:

`y-y_1=m(x-x_1)`

using point (3, 6) = (x1, y1)

y - 6 = 8/5(x - 3) or

y - 6 = 1.6(x -3)