Question

Which is the equation of the line that passes through the points (4,3) and (6,2)?

A. Y= x - 1
B. Y= 0.5x - 1
C. Y= -0.5x + 5
D. Y= -0.5x + 1

Answer 1

`\large \boxed{y = - 0.5x + 5}`

Explanation:

Goal

• Find the equation of the line.

Given

• Coordinate points which are (4,3) and (6,2).

Step 1

• Find the slope by using slope formula or rise over run.

`\large{m = (y_2-y_1)/(x_2-x_1) }`

Substitute the coordinate points in

`m = (3 - 2)/(4 - 6) \\ m = (1)/( - 2) \\ m = - (1)/(2) \longrightarrow - 0.5 \\ m = - 0.5`

Step 2

• Rewrite the equation in slope-intercept form by substituting m = -0.5

`\large{y = mx + b}`

Substitute m = -0.5

`y = - 0.5x + b`

Step 3

• Find the value of b by substituting any given coordinate points in the equation.

Substituting both coordinate points still give the same answer.

Step 3.1

• Substitute (4,3) in the equation.

`y = - 0.5x + b \\ 3 = - 0.5(4) + b \\ 3 = - 2.0 + b \\ 3 = - 2 + b \\ 3 + 2 = b \\ 5 = b`

Step 3.2

• Substitute (6,2) in the equation.

`y = - 0.5 x+ b \\ 2 = - 0.5(6) + b \\ 2 = - 3.0 + b \\ 2 = - 3 + b \\ 2 + 3 = b \\ 5 = b`

Step 4

• Rewrite the equation again by substituting the value of b.

`y = - 0.5x + b`

Substitute b = 5 in the equation.

`y = - 0.5x + 5`

Hence, the equation is y = -0.5x + 5