Question

4. Find the equation of the line that passes through the point (-2,5) and is parallel to the line7x - 2y =1.[A] - 2x + 5y = 1 [B] 7x +2y = 1 [C] 7x-2y = -24 [D] 7x-2y = 39

Answer 1

Answer:

Option C. 7x - 2y = -24

Explanations:

The equation of the line passing through the point (x₁, y₁) and parallel to the line y = mx + c is given by:

$y-y_{1\text{ }}=m(x-x_1)$

The given equation is:

7x - 2y = 1

This can be simplied as:

$\begin{gathered} 2y\text{ = 7x -1} \\ y\text{ = }\frac{7}{2}x\text{ - }\frac{1}{2} \end{gathered}$

The line is passing through the point (-2, 5)

The slope, m = 7/2

Substitute m = 7/2, x₁ = -2, and y₁ = 5 into the equation y - y₁ = m(x - x₁)

$\begin{gathered} y\text{ - 5 = }\frac{7}{2}(x\text{ -(-2))} \\ y\text{ - 5 = }\frac{7}{2}(x\text{ + 2)} \\ 2(y\text{ - 5) = }7(x+2) \\ 2y\text{ - 10 = 7x + 14} \\ 7x\text{ - 2y = -10 - 14} \\ 7x\text{ - 2y = -24} \end{gathered}$