Question

question 5
given graph represents the equation of the line ( 3x + 5y = 15 ). find the distance between the x and y - intercepts. give your answer as a radical or exact value.
( sqrt{14} )
( sqrt{34} )
( sqrt{19} )
( sqrt{8} )

Explanation:

Step1: Find the x - intercept

Set \(y = 0\) in the equation \(3x+5y = 15\).

$$
LATEXBLOCK0
$$

So, the x - intercept is \((5,0)\).

Step2: Find the y - intercept

Set \(x = 0\) in the equation \(3x + 5y=15\).

$$
LATEXBLOCK1
$$

So, the y - intercept is \((0,3)\).

Step3: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Let \((x_1,y_1)=(5,0)\) and \((x_2,y_2)=(0,3)\).

$$
LATEXBLOCK2
$$

Answer:

\(\sqrt{34}\)