To find the equation of the line parallel to the given line and making a specific x-intercept, follow these steps:
1. Identify the form of the given equation: The equation of the given line is [tex]\(5x + 4y = 18\)[/tex].
2. Form of the parallel line: A line parallel to the given line will have the same coefficients for [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. Therefore, the general form of the equation for the parallel line will be [tex]\(5x + 4y = C\)[/tex], where [tex]\(C\)[/tex] is a constant to be determined.
3. Determine the x-intercept: Since the line makes an intercept of 2 units on the x-axis, at the x-intercept, the value of [tex]\(y\)[/tex] is 0.
4. Substitute the x-intercept in the equation: Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 0\)[/tex] into the parallel line's equation:
[tex]\[
5(2) + 4(0) = C
\][/tex]
5. Simplify the equation: Calculate the value of [tex]\(C\)[/tex]:
[tex]\[
10 = C
\][/tex]
6. Write the final equation: With [tex]\(C = 10\)[/tex], the equation of the line parallel to the given line and making an x-intercept of 2 units is:
[tex]\[
5x + 4y = 10
\][/tex]
So, the equation of the line that is parallel to [tex]\(5x + 4y = 18\)[/tex] and makes an intercept of 2 units on the x-axis is [tex]\[
5x + 4y = 10
\][/tex].
