Question

How do you do this problem?

Answer 1

we need to find the x intercept and y intercept.

general form of the equation of the line

is y - y1 = m(x - x1) where m = slopeand (x1, y1) is a point on the line.

so y - 4 = -1/3( x - 3) is the equation of the line

y -intercept:- y - 4 = -1/3 (0 - 3)

y = 1 + 4 = 5

x intercept:- 0 - 4 = -1/3(x - 3)

1/3 x = 1 + 4 = 5

x = 15

So the area of the triangle = 1/2 * 5 * 15 = 37.5 answer

Answer 2

Remark

If you can find the x and y intercepts, then, because it is a right angle the base (the x intercept) and height (the y intercept) will be known. The given point will determine the exact line equation.

Step One

State what you know so far.

y = -(1/3)x + b

Step Two

Find b using the given point on the line.

(3,4) is the given point. That means when x = 3, y will be 4

y = -1/3 x + b

4 = -1/3 (3) + b Cancel the 3s

4 = - 1 + b Add 1 to both sides.

5 = b

The equation is now

y = -(1/3)x + 5

Step Three

Find the y intercept. The y intercept occurs when x = 0

y = -1/3(0) + 5

y = 5

The height = 5

Step Four

Find the x intercept. That occurs when y = 0

y = -(1/3)x + 5

0 = (-1/3) x + 5 Subtract 5 from both sides.

-5 = -1/3 x Multiply both sides by -3

-5 * - 3 = x

x = 15

Step 5

Find the area

base = 15

height = 5

Area = 1/2 * base * height.

Area = 1/2 * 15 * 5

Area = 1/2 * 75

Area = 37.5

Answer A