Match the equation with the line from the system shown on the graph.

Question

The graph shows two lines, one purple and one blue.
The purple line passes through the point (3, 2) and the blue line passes through the point (0, -2).
(2 points)
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Purple Line :

Blue Line :

Answer 1

To match the lines with their equations, we will need to determine the slopes and y-intercepts of each line based on the points they pass through.

For the Purple Line:

• Point: (3, 2)

To find the equation of this line, we need the slope. However, since we only have one point, we cannot determine the slope directly without additional information about another point on the same line. If we assume the purple line has a certain slope or if additional points are provided, we can use the point-slope form of the equation of a line \(y - y_1 = m(x - x_1)\).

Assuming we know the slope, we can compute the equation.

For the Blue Line:

• Point: (0, -2)

This point indicates that the y-intercept (b) of the blue line is -2. We still need the slope to find the complete equation, which again requires more information unless provided.

If we assume both lines are linear:

1. If we knew the slopes or other points on the opposite lines, they could lead to a more accurate answer.
2. Common forms include slope-intercept \(y = mx + b\) or forms derived from two points for the lines.

Assuming hypothetical slopes:

Let's say:

• The slope of the Purple Line is \(m_{purple}\).
• The slope for the Blue Line can also be assumed, let's say \(m_{blue}\).

Example Equations:

• For the purple line, if it had a slope of 'm':

  • \(y - 2 = m(x - 3)\) → Rearranging gives \(y = mx - 3m + 2\).

• For the blue line with a slope of 'n':

  • \(y = nx - 2\).

Give me the slopes or other points, or if we assume certain trends, and I could generate precise equations and match them effectively!