Question

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

Answer 1

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;

`y = ( - 1)/(2) x + (2)/(3)`

2nd equation..

Now, From equation (ii)

We have;

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

We get;

Slope = -1/2.

For perpendicular lines,

`m1 * m2 = - 1`

`m1 * ( - 1)/(2) = - 1`

Therefore the slope is 2.

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

`(y - 3) = 2(x - 2)`

Simplify them to get equation.

`(y - 3) = 2x - 4`

`y = 2x - 1`

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

Hope it helps..