Question

find the slope and y-intercept of the given line, and graph it.
3y = -7x
...
the slope of the line is $-\frac{7}{3}$
(simplify your answer. type an integer or a fraction.)
what is the y-intercept?
(type an ordered pair)

Explanation:

Step1: Recall the 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. The \(y\) - intercept is the point where the line crosses the \(y\) - axis, and at this point, \(x = 0\).

Step2: Rewrite the given equation in slope - intercept form

We are given the equation \(3y=-7x\). Divide both sides of the equation by 3 to solve for \(y\):
\(y=-\frac{7}{3}x+0\)

Step3: Find the \(y\) - intercept

In the slope - intercept form \(y = mx + b\), when \(x = 0\), \(y=b\). From the equation \(y =-\frac{7}{3}x + 0\), we can see that \(b = 0\). So the \(y\) - intercept occurs at the point \((0,0)\) (because when \(x = 0\), \(y=0\)).

Answer:

\((0,0)\)