The system of linear equations for lines f and g are y = x - 2 and y = 3x - 6, respectively.
To write a system of linear equations for lines f and g, we need to determine the slope (m) and the y-intercept (b) for each line using the given points.
Let's start with Line f:
The slope (mf) is calculated as (y2 - y1) / (x2 - x1) = (-1 - (-5)) / (-3 - (-7)) = 4 / 4 = 1.
Now, we can use the slope-intercept form y = mx + b to find the y-intercept bf using one of the points (let's use (-3, -1)):
-1 = 1 * (-3) + bf, which gives bf = -2.
So, the equation for Line f is y = x - 2.
Now, let's do the same for Line g:
The slope (mg) is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-12)) / (0 - (-2)) = 6 / 2 = 3.
Using the point (-2, -12):
-12 = 3 * (-2) + bg, which gives bg = -6.
So, the equation for Line g is y = 3x - 6.