Question

which linear function has the greatest \\(y\\)-intercept?

\\(x + 6y = 36\\)
\\(y = 15x + 5\\)
\\(3x + 8y = 24\\)
\\(y = 4x + 7\\)

Explanation:

Define the y-intercept of a line

To find the \(y\)-intercept of any linear function, we determine the value of \(y\) when \(x = 0\).

Find the y-intercept of the first option

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

Find the y-intercept of the second option

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Find the y-intercept of the third option

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK2
$$

Find the y-intercept of the fourth option

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK3
$$

Compare the y-intercept values

We compare the calculated \(y\)-intercepts:

• First option: \(y = 6\)
• Second option: \(y = 5\)
• Third option: \(y = 3\)
• Fourth option: \(y = 7\)

The greatest value is \(7\), which corresponds to the function \(y = 4x + 7\).

Answer:

• (A) \(x+6y=36\)
• (B) \(y=15x+5\)
• (C) \(3x+8y=24\)
• (D) \(y=4x+7\) (Correct answer)