Determine if the two lines are intersecting, parallel or the same lines by comparing the linear equations in slope - intercept form. State how many solutions there will be for each system.
Y= ½(x - 6)
Y= ½(x + 2) - 4
To determine the relationship between the two lines, we can compare their slopes and y-intercepts.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
For the first line, y = ½(x - 6), we can rewrite it as y = ½x - 3.
Comparing this to the second line, y = ½(x + 2) - 4, we see that they have the same slope, which is ½. However, their y-intercepts are different. The y-intercept of the first line is -3, while the y-intercept of the second line is -4.
Since the slopes are the same, but the y-intercepts are different, the lines are parallel. Parallel lines never intersect, so there are no solutions for this system.