Find the equation of the line which is parallel to the line 5x +4y=18 and makes an intercept of 2 units on the x-axis
To find the equation of a line that is parallel to a given line and makes an intercept on the x-axis, we need to determine two things: the slope of the parallel line and the x-intercept.
First, let's find the slope of the given line. We can put it in slope-intercept form (y = mx + b), where m is the slope:
5x + 4y = 18
Rearranging the equation:
4y = -5x + 18
y = (-5/4)x + 18/4
y = (-5/4)x + 9/2
From this equation, we can see that the slope of the given line is (-5/4).
Since the line we are looking for is parallel to the given line, it will also have the same slope of (-5/4).
Next, we need to find the x-intercept of the line. The x-intercept occurs when y = 0. We can substitute this into the slope-intercept form and solve for x:
0 = (-5/4)x + 9/2
Multiplying both sides by 4 to eliminate the fraction:
0 = -5x + 18
Rearranging the equation:
5x = 18
x = 18/5
So, the x-intercept is 18/5.
Now we have the slope (-5/4) and the x-intercept (18/5) of the line we are looking for. We can use this information to write the equation of the line in slope-intercept form:
y = (-5/4)x + b
To find the value of b, we substitute the x-intercept into the equation:
0 = (-5/4)(18/5) + b
Simplifying the equation:
0 = -9/2 + b
b = 9/2
Therefore, the equation of the line parallel to 5x + 4y = 18 and with an x-intercept of 2 units is:
y = (-5/4)x + 9/2