Question

date
(10) 3x - 2y = -16

Explanation:

Step1: Convert to slope - intercept form

We start with the equation \(3x - 2y=- 16\). 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).
First, subtract \(3x\) from both sides: \(-2y=-3x - 16\).
Then, divide each term by \(-2\): \(y=\frac{-3x}{-2}+\frac{-16}{-2}\), which simplifies to \(y = \frac{3}{2}x + 8\).

Step2: Find two points on the line

• Find the \(y\) - intercept: When \(x = 0\), substitute \(x = 0\) into \(y=\frac{3}{2}x + 8\). Then \(y=\frac{3}{2}(0)+8=8\). So one point is \((0,8)\). But looking at the given graph, the \(y\) - axis only goes up to \(6\) and down to \(-6\), so we need another point.
• Find the \(x\) - intercept: When \(y = 0\), substitute \(y = 0\) into the original equation \(3x-2y=-16\). We get \(3x-2(0)=-16\), so \(3x=-16\), and \(x =-\frac{16}{3}\approx - 5.33\). But this is also outside the visible range of the given graph. Let's find a point within the graph's range. Let's choose \(x=-4\). Substitute \(x = - 4\) into \(y=\frac{3}{2}x + 8\). Then \(y=\frac{3}{2}(-4)+8=-6 + 8 = 2\). So the point is \((-4,2)\). Let's choose \(x=-2\). Substitute \(x=-2\) into \(y=\frac{3}{2}x + 8\), \(y=\frac{3}{2}(-2)+8=-3 + 8 = 5\). Wait, maybe a better way: from \(y=\frac{3}{2}x + 8\), when \(x=-4\), \(y = 2\); when \(x=-2\), \(y = 5\); when \(x = 2\), \(y=\frac{3}{2}(2)+8=3 + 8 = 11\) (too big). Wait, maybe there is a mistake in my approach. Let's go back to the original equation \(3x-2y=-16\). Let's solve for \(x\) in terms of \(y\): \(3x=2y - 16\), \(x=\frac{2y-16}{3}\). Let's take \(y = 4\), then \(x=\frac{2(4)-16}{3}=\frac{8 - 16}{3}=\frac{-8}{3}\approx - 2.67\). Take \(y = 2\), \(x=\frac{2(2)-16}{3}=\frac{4 - 16}{3}=\frac{-12}{3}=-4\). So the point \((-4,2)\) is on the line. Take \(y = 5\), \(x=\frac{2(5)-16}{3}=\frac{10 - 16}{3}=\frac{-6}{3}=-2\). So the point \((-2,5)\) is on the line. Now, to graph the line, we can plot the points \((-4,2)\) and \((-2,5)\) (or other valid points within the grid) and draw a straight line through them.

(Note: Since the problem is about graphing the linear equation \(3x - 2y=-16\) on the given coordinate grid, after finding the equation in slope - intercept form and identifying points, we can plot the points and draw the line. The key steps are converting to slope - intercept form and finding points to plot.)

Answer:

To graph \(3x - 2y=-16\) (or \(y=\frac{3}{2}x + 8\)):

1. Identify the slope \(m=\frac{3}{2}\) and \(y\) - intercept \(b = 8\) (but adjust for the graph's range).
2. Plot points like \((-4,2)\) (when \(x=-4,y = 2\)) and \((-2,5)\) (when \(x=-2,y = 5\)) on the grid.
3. Draw a straight line through the plotted points.