Question

-3x + y = 6
a) graph of a line with slope 3, y-intercept 6
b) graph of a line with slope -1/4, y-intercept 2

Explanation:

Step1: Rewrite the equation in slope - intercept form

The given equation is \(-3x + y=6\). We can rewrite it in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
By adding \(3x\) to both sides of the equation \(-3x + y = 6\), we get \(y=3x + 6\).

Step2: Analyze the slope and y - intercept

For the equation \(y = 3x+6\), the slope \(m = 3\) (which is positive, so the line should be increasing from left to right) and the y - intercept \(b = 6\) (the line crosses the y - axis at \((0,6)\)).
Now let's analyze the graphs:

• Graph A: The line has a positive slope (increasing from left to right) and crosses the y - axis at \((0,6)\), which matches our slope - intercept form.
• Graph B: The line has a negative slope (decreasing from left to right) and crosses the y - axis at \((0,2)\), which does not match \(y = 3x + 6\).

Answer:

A) The graph with a line passing through \((0,6)\) and having a positive slope (increasing from left to right)