5x - 6y = -5
Explanations:The equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
y - y₁ = m (x - x₁)
where m is the slope of the line and is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
For the line passing through the points (-1, 0) and (5, 5)
[tex]\begin{gathered} x_1=-1,y_1=0,x_2=5,y_2=5 \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{5-0}{5-(-1)} \\ m\text{ = }\frac{5}{6} \end{gathered}[/tex]Substitute the values of x₁, y₁, and m into the equation of the line:
y - y₁ = m (x - x₁)
[tex]\begin{gathered} y\text{ - 0 = }\frac{5}{6}(x\text{ - (-1))} \\ y\text{ = }\frac{5}{6}\text{ (x + 1)} \\ y\text{ = }\frac{5}{6}x\text{ + }\frac{5}{6} \end{gathered}[/tex]6y = 5x + 5
5x - 6y = -5
The equation of the line is:
5x - 6y = -5
