Question

(11) 6x + 5y = -15

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(6x + 5y=-15\). We want to solve for \(y\) to get it in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
Subtract \(6x\) from both sides: \(5y=-6x - 15\).
Then divide each term by 5: \(y=\frac{-6x - 15}{5}=-\frac{6}{5}x-3\).

Step2: Find the \(y\) - intercept and a second point

The \(y\) - intercept \(b=-3\), so the line crosses the \(y\) - axis at \((0, - 3)\).
To find another point, we can use the slope. The slope \(m =-\frac{6}{5}\), which means for a run of 5 (change in \(x\) of 5), the rise is - 6 (change in \(y\) of - 6).
Starting from \((0,-3)\), if we move 5 units to the right (increase \(x\) by 5: \(x = 0 + 5=5\)) and 6 units down (decrease \(y\) by 6: \(y=-3-6 = - 9\))? Wait, no, maybe it's easier to use \(x =-\frac{5}{2}\) (when \(y = 0\))? Wait, let's find the \(x\) - intercept. Set \(y = 0\) in \(6x+5y=-15\), then \(6x=-15\), so \(x=-\frac{15}{6}=-\frac{5}{2}=-2.5\). So the \(x\) - intercept is at \((-\frac{5}{2},0)\) or \((-2.5,0)\) and the \(y\) - intercept is at \((0, - 3)\).
We can plot the points \((0,-3)\) and \((-2.5,0)\) on the grid. The line passing through these two points is the graph of \(6x + 5y=-15\).
(If we were to draw the line: from \((0,-3)\), since the slope is \(-\frac{6}{5}\), for every 5 units we move to the right along the \(x\) - axis, we move 6 units down along the \(y\) - axis, or for every 5 units we move to the left, we move 6 units up.)

Answer:

To graph \(6x + 5y=-15\) (or \(y =-\frac{6}{5}x - 3\)):

1. Plot the \(y\) - intercept \((0,-3)\) (where the line crosses the \(y\) - axis).
2. Plot the \(x\) - intercept \((-\frac{5}{2},0)\) (or \((-2.5,0)\)) (where the line crosses the \(x\) - axis).
3. Draw a straight line through these two points. The line should have a slope of \(-\frac{6}{5}\), meaning it is a line that goes down from left to right (since the slope is negative) with a "rise" of - 6 and a "run" of 5 (or "rise" of 6 and "run" of - 5).