Question

a certain line is defined by the equation
$y = \frac{5x - 8}{2}$
what is the value of the slope?
$m = $
what is the $y$-intercept of the line?
$b = $
which graph correctly represents the line?

Explanation:

For finding the slope:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
We are given the equation \(y=\frac{5x - 8}{2}\). We can rewrite this equation by distributing the division by 2.

Step2: Simplify the given equation

\(y=\frac{5x}{2}-\frac{8}{2}\), which simplifies to \(y=\frac{5}{2}x-4\).
Comparing this with the slope - intercept form \(y = mx + b\), we can see that the coefficient of \(x\) (which is the slope \(m\)) is \(\frac{5}{2}\).

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(b\) is the \(y\) - intercept.
We have the equation \(y=\frac{5x - 8}{2}\). After simplifying it (as we did above) to \(y=\frac{5}{2}x - 4\).

Step2: Identify the \(y\) - intercept

Comparing \(y=\frac{5}{2}x-4\) with \(y = mx + b\), we can see that the value of \(b\) (the \(y\) - intercept) is \(- 4\).

Answer:

The value of the slope \(m=\frac{5}{2}\)

For finding the \(y\) - intercept: