Question

1. a line is described by the equation $y = \frac{3}{5}x + \frac{4}{7}$ in slope - intercept form. identify the slope and $y$-intercept of the line.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is given by \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the \(y\) - intercept (the value of \(y\) when \(x = 0\), and the point is \((0,b)\)).

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

The given equation is \(y=\frac{3}{5}x+\frac{4}{7}\). Comparing this equation with the slope - intercept form \(y = mx + b\), we can see that the coefficient of \(x\) (which is \(m\)) is \(\frac{3}{5}\) and the constant term (which is \(b\)) is \(\frac{4}{7}\).

Answer:

The slope of the line is \(\frac{3}{5}\) and the \(y\) - intercept is \(\frac{4}{7}\) (or the \(y\) - intercept is the point \((0,\frac{4}{7})\)).