Answer:
[tex] \large \boxed{y = - 2x + 3}[/tex]
Step-by-step explanation:
Goal
- Write the equation of a line with given coordinate points
Given
- Coordinate points which are (0,3) and (-4,11).
Step 1
- Use the slope formula also known as rise over run to calculate the slope.
[tex] \large \boxed{m = \frac{y_2-y_1}{x_2-x_1} }[/tex]
Substitute coordinate points in.
[tex]m = \frac{11 - 3}{ - 4 - 0} \\ m = \frac{8}{ - 4} \longrightarrow \frac{2}{ - 1} \\ m = - 2[/tex]
Step 2
- Substitute the value of slope in the slope-intercept form.
[tex] \large \boxed{y = mx + b}[/tex]
where m = slope and b = y-intercept.
[tex]y = - 2x + b[/tex]
Step 3
- Substitute any given coordinate points in the new equation to find the value of b.
Substitute both coordinate points still give the same solution.
Step 3.1 — (0,3)
[tex]y = - 2x + b \\ 3 = - 2(0) + b \\ 3 = 0 + b \\ 3 = b[/tex]
Step 3.2 — (-4,11)
[tex]y = - 2x + b \\ 11 = - 2( - 4) + b \\ 11 - 8 = b \\ 3 = b[/tex]
Therefore, the value of b is 3.
Step 4
- Substitute the value of b in the equation.
[tex]y = - 2x + b \\ y = - 2x + 3[/tex]
Hence, the equation of a line is y = -2x+3.
