Answer:



Explanation:
Part (a)
To find the equation of the line passing through the points (-2, -1) and (5, -3), first calculate its slope (m) using the slope formula:

Substitute the two points into the formula:

Now, substitute the slope (m) and one of the points (-2, -1) into the point-slope form of a linear equation, then rearrange the equation to isolate y to write the equation in slope-intercept form:

So, the equation of the line in slope-intercept form is:


Part (b)
To find the equation of the line passing through (2, 3) and perpendicular to the line defined by 2x = -4y, we first need to find the slope of the given line.
Rearrange 2x = -4y to slope-intercept form:

Therefore, the slope of the line is -1/2.
If two lines are perpendicular to each other, their slopes are negative reciprocals. Therefore, the slope (m) of the perpendicular line is:

Now, substitute the found slope (m = 2) and the point the line passes through (2, 3) into the point-slope form of a linear equation, then rearrange the equation to isolate y to write the equation in slope-intercept form:

So, the equation of the line passing through (2, 3) and perpendicular to 2x = -4y is:


Part (c)
A line parallel to the y-axis is a vertical line.
Vertical lines have the equation of the form x = a, where a is a constant.
In this case, the line passes through the point (-4/5, 1/7), so the equation of the line is:

Note: There's no need to change this equation since it is already in a form that describes a vertical line parallel to the y-axis.