Respuesta :
Line equation
We know the line equation is expressed by
y = mx + b, where is m is its slope (how inclinated it is) and b is intercept with the y-axis.
Finding m
We find its inclination, its slope, m, by
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ =\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Let's say
(x₁, y₁) = (-6, 5)
(x₂, y₂) = (-3, 3)
Then
[tex]\begin{gathered} m=\frac{3-5}{-3-(-6)} \\ =\frac{-2}{-3+6}=\frac{-2}{3} \\ m=-\frac{2}{3} \end{gathered}[/tex]Then y = -(2/3)x + b,
Finding b
Since b is intercept with the y-axis, we know it intercepts y when x = 0
Using the equation we have found y = -(2/3)x + b, and replacing one point given by the question (x₂, y₂) = (-3, 3)
y = -(2/3)x + b
3 = -(2/3)(-3) + b
3 = -2 + b
3 + 2 = b
Then, b = 5
Therefore,
Answer, y = -(2/3)x + 5,
