Final answer:
To find the equation of a line parallel to 5x + 4y = 18 and with a y-intercept of 2, we need to determine the slope of the given line. The slope-intercept form of a line is then used to find the equation. The equation of the line is y = (-5/4)x + 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. The equation of a line in the form y = mx + b, where m represents the slope. Rearranging the given equation, we get 4y = -5x + 18, and dividing by 4, we find y = (-5/4)x + 18/4. Therefore, the slope of the given line is -5/4.
Since we want to find a line parallel to this, the slope of the new line will also be -5/4. Now, we are given that the new line makes an intercept of 2 units on the y-axis. The y-intercept, represented by the coordinate (0, b), where b is the intercept, is the point where the line intersects the y-axis. So, we now have the point (0, 2) on the new line.
Using the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values we have found to get the equation of the new line. Plugging in the slope (-5/4) and the y-intercept (2), the equation of the line parallel to 5x + 4y = 18 with a y-intercept of 2 is y = (-5/4)x + 2.