To write the equation of a line that goes through the point (3,2) and has a y-intercept of 1, we can use the point-slope form of a line. The point-slope form is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line. The slope is a measure of the steepness of the line, and it is calculated as the rise (the change in y) over the run (the change in x).
To find the slope of the line, we can use the two points (3,2) and (3,1). The rise is 1 - 2 = -1 and the run is 3 - 3 = 0, so the slope is -1/0, which is undefined. This means that the line is a vertical line and does not have a slope.
Since the line is a vertical line, we cannot use the point-slope form to write its equation. Instead, we can use the slope-intercept form, which is:
y = mx + b
Where m is the slope of the line and b is the y-intercept. In this case, the slope is 0 (since the line is vertical), and the y-intercept is 1, so the equation of the line is:
y = 0x + 1
To write the equation of a line that is perpendicular to line a and goes through the point (-4,2), we need to find the slope of line a. Since line a is a vertical line, its slope is undefined. However, we know that the slope of a line perpendicular to it must be 0.
Using the point-slope form, the equation of line b is:
y - 2 = 0(x - (-4))
Simplifying, we get:
y = 0x + 2
So, the equation of line b is:
y = 0x + 2