Question

Find the equation of the given line.Find the equation of the line passing through (1, 4) and (-6, 9).y =

Answer 1

Answer:

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:

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_(_1)) \\ m\text{ = }(9-4)/(-6-1) \\ m\text{ = }(5)/(-7) \\ m\text{ = }(-5)/(7) \end{gathered}`

Substituting the values of m, x₁, and y₁ into the general equation of a line:

`\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }(-5)/(7)(x\text{ - 1)} \\ y\text{ - 4 = }(-5)/(7)x\text{ + }(5)/(7) \\ y\text{ = }(-5)/(7)x\text{ + }(5)/(7)+\text{ 4} \\ y\text{ = }(-5)/(7)x\text{ + }(33)/(7) \\ 7y\text{ = -5x + }33 \end{gathered}`

The equation of the line is 7y = -5x + 33