Question

state the slope and the y-intercept for the graph:
$y = -\frac{3}{7}x - \frac{1}{7}$
options:
$m = -\frac{1}{7}$ $b = -\frac{3}{7}$
$m = 7$ $b(7, 0)$
$m = -\frac{3}{7}$ $b(-\frac{1}{7}, 0)$
$m = -\frac{3}{7}$ $b(0, -\frac{1}{7})$

Explanation:

Step1: Recall Slope-Intercept Form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. The \(y\) - intercept is the point where the line crosses the \(y\) - axis, and at this point, \(x = 0\), so the coordinates of the \(y\) - intercept are \((0,b)\).

Step2: Identify \(m\) and \(b\) from the given equation

Given the equation \(y=-\frac{3}{7}x-\frac{1}{7}\). Comparing it with \(y = mx + b\), we can see that the coefficient of \(x\) (which is \(m\)) is \(-\frac{3}{7}\), and the constant term (which is \(b\)) is \(-\frac{1}{7}\). So the slope \(m = -\frac{3}{7}\) and the \(y\) - intercept is the point \((0,-\frac{1}{7})\) (since when \(x = 0\), \(y=b=-\frac{1}{7}\)).

Answer:

D. \(m = -\frac{3}{7}\) \(b(0,-\frac{1}{7})\) (assuming the last option is labeled D, if we follow the order of the options as presented: first option is about wrong \(m\) and \(b\), second option has wrong \(m\) and wrong interpretation of \(b\) (it's giving an \(x\) - intercept - like point), third option gives an \(x\) - intercept instead of \(y\) - intercept, and the last option has correct \(m\) and correct \(y\) - intercept point)