Question

Graph the line that passes through the points (4, 3) and (1,6) and determine the equation of the line.

Answer 1

y = -x + 7

Explanation:

(x1, y1) = (4 , 3)

(x2, y2) = (1 , 6)

`slope=\frac{y_(2)-y{1}}{x_(2)-x_(1)}\\\\=(6-3)/(1-4)\\\\=(3)/(-3)\\\\=-1\\\\y-y_(1)=m(x-x_(1))\\\\`

m = - 1; (4,3)

y - 3 = (-1)(x -4)

y - 3 = -x + 4

y = -x + 4 + 3

y = -x + 7

Answer 2

y = -x + 7

Explanation:

Slope-Intercept Form: y = mx + b

Slope Formula:
`m = (y2-y1)/(x2-x1)`

Step 1: Find slope

m = (6 - 3)/(1 - 4)

m = -1

Step 2: Find b

y = -x + b

6 = -1 + b

b = 7

Step 3: Rewrite linear equation

y = -x + 7