7y = - 5x + 33
Explanations:The line is passing through the points (1, 4) and (-6, 9)
The general equation a line passing through the points (x₁ ,y₁ ) and (x₂ , y₂) is written as:
y - y₁ = m (x - x₁)
x₁ = 1, x₂ = -6, y₁ = 4, y₂ = 9
where m is the slope of the line.
The slope m is calculated using the formula:
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_{_1}} \\ m\text{ = }\frac{9-4}{-6-1} \\ m\text{ = }\frac{5}{-7} \\ m\text{ = }\frac{-5}{7} \end{gathered}[/tex]Substituting the values of m, x₁, and y₁ into the general equation of a line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }\frac{-5}{7}(x\text{ - 1)} \\ y\text{ - 4 = }\frac{-5}{7}x\text{ + }\frac{5}{7} \\ y\text{ = }\frac{-5}{7}x\text{ + }\frac{5}{7}+\text{ 4} \\ y\text{ = }\frac{-5}{7}x\text{ + }\frac{33}{7} \\ 7y\text{ = -5x + }33 \end{gathered}[/tex]The equation of the line is 7y = -5x + 33
