Question

May someone please help me with this im very confused on how to solve this

Answer 1

4y - 5x + 7 = 0

Explanation:

To get to the equation of its perpendicular, firstly we'll need the slope of this line.

`\boxed{ \mathfrak{slope = \red{ \mathsf{ (y_(2) - y _(1))/(x_(2) - x _(1)) }}}}`

(x1, y1) and (x2, y2) are any two points kn the given line.

I caught two points that lie on this graph, and they are :

• (-2, 2)
• (8, -6)

`\mathsf{ \implies \: slope = (y_(2) - y _(1))/(x_(2) - x _(1)) }`

`\mathsf{ \implies \: slope = ( - 6- 2)/(8 - ( - 2)) }`

`\mathsf{ \implies \: slope = ( -8)/(8 + 2) }`

(two minus make a plus)

`\mathsf{ \implies \: slope = ( -8)/(10) }`

`\mathsf{ \implies \: slope = \frac{ \cancel{-8} {}^( \: \: - 4) }{ \cancel{10} \: \: {}^(5) } }`

slope = -4 /5

That's the slope of the given line.

Now, the slope of the line perpendicular to this one will be equal to its negative reciprocal.

slope (perpendicular) = 5/ 4

and they've given a point that lies in the perpendicular, it is = (3, 2)

For equation of a line thru a point, we have:

`\boxed{ \mathsf{ \red {y} - {y}^(1) = slope * (\red{x} - {x}^(1) }) }`

the letters in red are the variables that won't be changed thruout.

and (x¹, y¹) are the points on the line.

• (x¹, y¹) = (3, 2)
• slope = 5/ 4

`\implies \mathsf{y - 2 = (5)/(4) * (x - 3) }`

`\implies \mathsf{(y - 2)4 = 5x - 15}`

`\implies \mathsf{4y - 8 = 5x - 15}`

`\implies \mathsf{(4y - 5x) - 8 + 15 = 0}`

`\implies \mathsf{4y - 5x + 7 = 0}`

and thats the required equation of the perpendicular.