Question

Write an equation for a line perpendicular to Y equals negative 3X -2 and passing through the point (9,7)

Answer 1

The equation for line perpendicular to y = -3x - 2 and passing through the point (9,7)  in slope intercept form is:

$y = \frac{x}{3}+4$

Solution:

Given that we have to write the equation for line perpendicular to y = -3x - 2 and passing through the point (9,7)

Let us first find the slope of line

The equation of line in slope intercept form is given as:

y = mx + c -------- eqn 1

Where, "m" is the slope of line and "c" is the y - intercept

Given equation of line is:

y = -3x - 2

On comparing the above equation with eqn 1

m = -3

We know that product of slope of a line and line perpendicular to it is equal to -1

Therefore,

$-3 \times \text{ slope of line perpendicular to given line } = -1\\\\\text{ slope of line perpendicular to given line } = \frac{1}{3}$

Now find the equation of line passing through the point (9, 7)

$\text{Substitute } (x, y) = (9, 7) \text{ and } m = \frac{1}{3} \text{ in eqn 1 }$

$7 = \frac{1}{3} \times 9+c\\\\7=3+c\\\\c = 4$

$\text{Substitute } m = \frac{1}{3} \text{ and } c = 4 \text{ in eqn 1 }$

$y = \frac{1}{3}x+4\\\\y = \frac{x}{3}+4$

Thus the equation of line in slope intercept form is found