Question

graph this line:
y + 2 = x + 9
click to select points on the graph.

Explanation:

Step1: Rewrite the equation in slope - intercept form

We start with the equation \(y + 2=x + 9\). To get it in the form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), we subtract 2 from both sides of the equation.
\(y+2 - 2=x + 9-2\)
\(y=x + 7\)
The slope \(m = 1\) and the y - intercept \(b = 7\).

Step2: Find two points on the line

• Y - intercept point: When \(x = 0\), we substitute \(x = 0\) into \(y=x + 7\). Then \(y=0 + 7=7\). So one point is \((0,7)\).
• Another point: Let's choose \(x = 1\). Substitute \(x = 1\) into \(y=x + 7\), we get \(y=1 + 7 = 8\). So another point is \((1,8)\). We can also choose \(x=- 7\), then \(y=-7 + 7=0\), so the point \((-7,0)\) is also on the line.

To graph the line, we can plot the points \((0,7)\) (on the y - axis, 7 units up from the origin) and \((-7,0)\) (on the x - axis, 7 units to the left of the origin) or \((1,8)\) and then draw a straight line through them.

Answer:

To graph the line \(y=x + 7\) (derived from \(y + 2=x + 9\)):

• Plot the y - intercept at \((0,7)\).
• Plot another point, for example, when \(x=-7\), \(y = 0\) (point \((-7,0)\)) or when \(x = 1\), \(y = 8\) (point \((1,8)\)).
• Draw a straight line through the plotted points.