Question

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

Answer 1

Answer:

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

Step-by-step 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.

$\large{m = \frac{y_2-y_1}{x_2-x_1} }$

Substitute the coordinate points in

$m = \frac{3 - 2}{4 - 6} \\ m = \frac{1}{ - 2} \\ m = - \frac{1}{2} \longrightarrow - 0.5 \\ m = - 0.5$

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