Answer :
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)
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:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} m\text{ =}\frac{14-6}{8-3}\text{ = }\frac{8}{5} \\ m\text{ = 8/5} \end{gathered}[/tex]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:
[tex]y-y_1=m(x-x_1)[/tex]using point (3, 6) = (x1, y1)
y - 6 = 8/5(x - 3) or
y - 6 = 1.6(x -3)