Question

Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5,-4)? Select
three options.

Answer 1

Answer:

The equation of line passing through points (5 , - 4) is 2 x + 5 y + 10 = 0

Step-by-step explanation:

Given equation of line as

5 x - 2 y = - 6

Now, equation of line in standard form is y = m x + c

where m is the slope

So, 5 x - 2 y = - 6

Or, 2 y = 5 x + 6

Or, y = $\frac{5}{2}$ x + 3

So, Slope of this line m = $\frac{5}{2}$

Again , let the slope of other line passing through point (5 , - 4) is M

And Both lines are perpendicular , So , products of line = - 1

i.e m × M = - 1

Or, M = - $\frac{1}{m}$

Or, M = - $\frac{1}{\frac{5}{2}}$ = - $\frac{2}{5}$

So, equation of line with slope M and points (5, - 4) is

y - $y_1$ = M × (x - $x_1$)

Or, y - ( - 4 ) = - $\frac{2}{5}$ × ( x - 5 )

Or, y + 4 = - $\frac{2}{5}$ x + $\frac{2}{5}$ × 5

Or, y + 4 =  - $\frac{2}{5}$ x + 2

or, y + 4 - 2 =  - $\frac{2}{5}$ x

or, y + 2 =  - $\frac{2}{5}$ x

Or, 5×(y + 2) = - 2 x

∴ 5 y + 10 = - 2 x

I.e 2 x + 5 y + 10 = 0

Hence The equation of line passing through points (5 , - 4) is 2 x + 5 y + 10 = 0   Answer

Answer 2

Answer:

WRONG!

y = –Two-fifthsx – 2  * correct

2x + 5y = −10  * Correct

2x − 5y = −10

y + 4 = –Two-fifths(x – 5) * Correct

y – 4 = Five-halves(x + 5)

Step-by-step explanation: