Question

Write an equation of the line satisfying the given conditions. Through (2, -5), parallel to 5x 6y + 7

Answer 1

We have to determine the equation of the line passing through the point (2,-5) and parallel to the line $5x = 6y+7$

When two lines are parallel, then the slopes of the two lines are equal.

Equation of line with point $(x_1, y_1)$ and slope 'm' is given by:

$(y-y_1) = m(x-x_1)$

Since, we have to determine the equation of a line with point (2,-5).

So, the equation of the line is : $(y-(-5)) = m(x-2)$

$y+5 = m(x-2)$

Since, the line is parallel to the line $5x = 6y+ 7$

So, $6y +7 = 5x$

$6y = 5x - 7$

$y = \frac{5}{6}x - \frac{7}{6}$

So, slope of the line  'm' is $\frac{5}{6}$.

Therefore, the equation of the line is:

$(y+5) = \frac{5}{6}(x-2)$

$6y + 30 = 5x - 10$

$6y - 5x = -10-30$

$6y - 5x = -40$

Therefore, $6y - 5x = -40$ is the required equation of the line.