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 point where \(x = 0\), so the coordinate is \((0,b)\)).

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

Given the equation \(y=-\frac{3}{7}x-\frac{1}{7}\), comparing it with \(y = mx + b\):

• The coefficient of \(x\) is \(m = -\frac{3}{7}\).
• The constant term is \(b=-\frac{1}{7}\), and the \(y\)-intercept is the point \((0,-\frac{1}{7})\) since when \(x = 0\), \(y=b\).

Answer:

m\(=-\frac{3}{7}\) b\((0,-\frac{1}{7})\) (the fourth option: m\(=-\frac{3}{7}\) b\((0,-\frac{1}{7})\))