Question

what are the slope and the y-intercept of the linear function that is represented by the equation \\(8x - 2y = 5\\)?

• the slope is \\(-\frac{5}{2}\\), and the y-intercept is 4.
• the slope is \\(\frac{5}{2}\\), and the y-intercept is 4.
• the slope is 4, and the y-intercept is \\(-\frac{5}{2}\\).
• the slope is 4, and the y-intercept is \\(\frac{5}{2}\\).

Explanation:

Identify the given equation

We are given the linear equation:

$$8x - 2y = 5$$

Convert to slope-intercept form

Using the Slope of a Line knowledge point

$$
LATEXBLOCK0
$$

Identify slope and y-intercept

The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Comparing \(y = 4x - \frac{5}{2}\) to \(y = mx + b\):

• Slope \(m = 4\)
• y-intercept \(b = -\frac{5}{2}\)

Answer:

• The slope is \(-\frac{5}{2}\), and the y-intercept is 4.
• The slope is \(\frac{5}{2}\), and the y-intercept is 4.
• The slope is 4, and the y-intercept is \(-\frac{5}{2}\). (Correct answer)
• The slope is 4, and the y-intercept is \(\frac{5}{2}\).