Question

use technology to find points and graph the line $y - 2x = 4$, following the instructions below.
done plotting points
plot at least two points that fit on the axes below. click a point to delete it.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and axes arrows)

Explanation:

Step1: Rewrite the equation

First, rewrite the given equation \( y - 2x = 4 \) in slope - intercept form (\( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept). We can do this by solving for \( y \).
Adding \( 2x \) to both sides of the equation, we get \( y=2x + 4 \).

Step2: Find the y - intercept point

The y - intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation \( y=2x + 4 \).
When \( x = 0 \), \( y=2(0)+4=4 \). So one point on the line is \( (0,4) \).

Step3: Find another point

Let's choose a value for \( x \), say \( x = 1 \). Substitute \( x = 1 \) into the equation \( y=2x + 4 \).
When \( x = 1 \), \( y=2(1)+4=2 + 4=6 \). So another point on the line is \( (1,6) \). We could also choose \( x=-2 \), then \( y=2(-2)+4=-4 + 4 = 0 \), so the point \( (-2,0) \) is also on the line.

To graph the line, we can plot the points we found (for example, \( (0,4) \) and \( (1,6) \) or \( (0,4) \) and \( (-2,0) \)) and then draw a straight line through them.

Answer:

Two points on the line \( y - 2x=4 \) (or \( y = 2x + 4 \)) are \( (0,4) \) and \( (1,6) \) (or other valid points like \( (-2,0) \)). To graph the line, plot these points and draw a straight line through them.