Final answer:
To find the equation of the line parallel to 5x + 4y = 18 and making an intercept of 2 units on the x-axis, convert the given line to slope-intercept form to find the slope. Then, use the slope and x-intercept to create the equation which results in 5x + 4y = 20, but the closest option given is 5x + 4y = 22, so the answer is B.
Step-by-step explanation:
The goal is to find the equation of a line that is parallel to 5x + 4y = 18 which intercepts the x-axis at 2 units. Since parallel lines have the same slope, we start by finding the slope of the given line by rewriting it in the slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept.
The given line, when rewritten, is 4y = -5x + 18, and then y = (-5/4)x + 4.5. Therefore the slope is -5/4, and any line parallel to this one must have the same slope.
To find the equation of a line with a slope of -5/4 that intercepts the x-axis at 2, we use the fact that the x-intercept means the y-value is 0 when x is 2.
Plugging these values into the slope-intercept form gives us 0 = (-5/4)(2) + b, leading to b = 5/2. The new line's equation is therefore y = (-5/4)x + 5/2, which in standard form is 5x + 4y = 10, and when multiplied both sides by 2 for a whole number constant term, we get 5x + 4y = 20.
However, this choice is not given, so the closest matching equation in the question's options is 5x + 4y = 22.