SOLUTION: Find the x-intercept of the straight line passing through P = (2, 3) and perpendicular to y + 3x = 8 .

Question 397155: Find the x-intercept of the straight line
passing through P = (2, 3) and perpendicular
to
y + 3x = 8 .
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point

.

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 3 to both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation of the line perpendicular to that goes through the point

is .

Here's a graph to visually verify our answer:

Graph of the original equation (red) and the perpendicular line (green) through the point

.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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