To determine a line that is parallel or perpendicular to another line, we need to determine the slope of the given line. The equation of a line in slope-intercept form is y = mx + b, where m represents the slope of the line.
In the equation y = (1/2)x + 7, the slope of the line is 1/2. Parallel lines have the same slope, so a line parallel to this equation will also have a slope of 1/2.
For the equation y = -2x - 3, the slope is -2. Perpendicular lines have slopes that are negative reciprocals of each other. So, to find a line perpendicular to this equation, we need to flip the slope and change the sign. In this case, the perpendicular line will have a slope of 1/2.
To find the x-intercept of an equation, we set y = 0 and solve for x. The x-coordinate of the x-intercept represents the point where the line crosses the x-axis.
Let's find the x-intercept for the equation 3x + 2y = 7:
Setting y = 0, we get:
3x + 2(0) = 7
3x = 7
Dividing both sides by 3, we find:
x = 7/3
So the x-intercept for this equation is (7/3, 0).
Now, let's find the x-intercept for the equation 2x + 3y = 7:
Setting y = 0, we have:
2x + 3(0) = 7
2x = 7
Dividing both sides by 2, we get:
x = 7/2
So the x-intercept for this equation is (7/2, 0).
Therefore, the x-intercepts of the two equations are (7/3, 0) and (7/2, 0) respectively.