Question

use technology to find points and graph the line $-3x - 4y = 16$, following the instructions below.
plot at least two points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Rewrite the equation

First, we assume the equation is \(-3x - 4y = 16\) (since the original might have a typo, missing the equal sign). Let's solve for \(y\) in terms of \(x\) or find intercepts.

Step2: Find x - intercept (y = 0)

Set \(y = 0\) in \(-3x - 4y = 16\), then \(-3x=16\), \(x =-\frac{16}{3}\approx - 5.33\). But maybe easier to find integer points. Let's rearrange the equation: \(4y=-3x - 16\), \(y =-\frac{3}{4}x - 4\).

Step3: Find two points

• When \(x = 0\): \(y=-\frac{3}{4}(0)-4=-4\), so point \((0, - 4)\).
• When \(x=-4\): \(y =-\frac{3}{4}(-4)-4 = 3 - 4=-1\), so point \((-4, - 1)\).
• Or when \(x = 4\): \(y=-\frac{3}{4}(4)-4=-3 - 4=-7\), point \((4, - 7)\).

We can plot points like \((0, - 4)\) and \((-4, - 1)\) (or other valid points from the equation) on the graph.

Answer:

Two points on the line \(-3x - 4y = 16\) (assuming the equation) are \((0, - 4)\) and \((-4, - 1)\) (plot these points on the given coordinate system).