Use the image to answer the question.

Question

Two lines intersect on the coordinate plane. Both axes range from negative 10 to 10 in increments of 1.
dotted line intercects with full line at 1, 5
dotted line 0,3
full line 0,0
What is the system of equations shown in the graph?

(2 points)
The equation of the solid line is y=

x
.

The equation of the dotted line is y=

x
+
.

Answer 1

To find the equations of the two lines based on the given information:

1. Full Line: The solid line intersects the y-axis at (0, 0) and intersects the dotted line at (1, 5). To determine the slope, we can use the points (0, 0) and (1, 5):

   • Slope (m) = (y2 - y1) / (x2 - x1) = (5 - 0) / (1 - 0) = 5
   • The equation of the solid line that passes through the origin with a slope of 5 is:

   \[ y = 5x \]

2. Dotted Line: The dotted line intersects the y-axis at (0, 3) and also intersects the solid line at (1, 5). We can again use the slope formula to find the slope of the dotted line using the points (0, 3) and (1, 5):

   • Slope (m) = (5 - 3) / (1 - 0) = 2
   • Using the point-slope form (y - y1 = m(x - x1)) using point (0, 3):

   \[ y - 3 = 2(x - 0) \]

   Simplifying gives:

   \[ y = 2x + 3 \]

So, the system of equations is:

• The equation of the solid line is \( y = 5x \).
• The equation of the dotted line is \( y = 2x + 3 \).