Final answer:
To find the equation of a line parallel to 5x + 4y = 18, use the slope-intercept form and the given intercept on the x-axis. The equation of the line is y = (-5/4)x + 5/2.
Step-by-step explanation:
To find the equation of a line parallel to the line 5x + 4y = 18, we need to determine the slope of the given line. We can rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept. By rearranging the equation, we get 4y = -5x + 18, and dividing both sides by 4, we have y = (-5/4)x + 18/4. Therefore, the slope of the given line is -5/4.
A line parallel to the given line will have the same slope. So, the slope of the parallel line is also -5/4. We also know that the line makes an intercept of 2 units on the x-axis, which means it intersects the x-axis at the point (2,0).
Using the slope-intercept form, y = mx + b, we can substitute the values of the slope (-5/4) and the x-intercept (2) to find the equation of the parallel line. Plugging in the values, we have 0 = (-5/4)(2) + b. Simplifying, we get 0 = -5/2 + b. Adding 5/2 to both sides, we get b = 5/2.
Therefore, the equation of the line that is parallel to 5x + 4y = 18 and makes an intercept of 2 units on the x-axis is y = (-5/4)x + 5/2.