Answer:
[tex] \large \boxed{y = - 0.5x + 5}[/tex]
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.
[tex] \large{m = \frac{y_2-y_1}{x_2-x_1} }[/tex]
Substitute the coordinate points in
[tex]m = \frac{3 - 2}{4 - 6} \\ m = \frac{1}{ - 2} \\ m = - \frac{1}{2} \longrightarrow - 0.5 \\ m = - 0.5[/tex]
Step 2
- Rewrite the equation in slope-intercept form by substituting m = -0.5
[tex] \large{y = mx + b}[/tex]
Substitute m = -0.5
[tex]y = - 0.5x + b[/tex]
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.
[tex]y = - 0.5x + b \\ 3 = - 0.5(4) + b \\ 3 = - 2.0 + b \\ 3 = - 2 + b \\ 3 + 2 = b \\ 5 = b[/tex]
Step 3.2
- Substitute (6,2) in the equation.
[tex]y = - 0.5 x+ b \\ 2 = - 0.5(6) + b \\ 2 = - 3.0 + b \\ 2 = - 3 + b \\ 2 + 3 = b \\ 5 = b[/tex]
Step 4
- Rewrite the equation again by substituting the value of b.
[tex]y = - 0.5x + b[/tex]
Substitute b = 5 in the equation.
[tex]y = - 0.5x + 5[/tex]
Hence, the equation is y = -0.5x + 5
