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write an equation in slope intercept form for the line described. perpendicular to y = -1/2x + 2/3, passes through (2,3)

Respuesta :

Sueraiuka

Step-by-step explanation:

Hey there!

Follow the steps to get answer.

  • Use one point formula and find 1st equation.
  • After that you find the slope of second equation.
  • Use the condition of perpendicular lines and find the slope of first equation.
  • Put slope value of equation in equation (i) and simplify them to get equation.

The equation of a line passing through point (2,3) is;

(y-3)= m1(x-2).......(i).

Another equation is;

[tex]y = \frac{ - 1}{2} x + \frac{2}{3} [/tex]

2nd equation..

Now, From equation (ii)

We have;

Comparing equation (ii) with y = mx+c.

We get;

Slope = -1/2.

For perpendicular lines,

[tex]m1 \times m2 = - 1[/tex]

[tex]m1 \times \frac{ - 1}{2} = - 1[/tex]

Therefore the slope is 2.

Put value of slope (m1) in equation (i). We get;

[tex](y - 3) = 2(x - 2)[/tex]

Simplify them to get equation.

[tex](y - 3) = 2x - 4[/tex]

[tex]y = 2x - 1[/tex]

Therefore the required equation is y = 2x-1.

Hope it helps..

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