find the equation of the line which is parallel to the 5x+4y=18 and makes on the intercept of 2 units on the x axis
Since your new line is parallel to the old one,
the new one has to be
5x+4y= c , that is, it will differ only in the constant
since you gave me that x = 2 when y = 0
sub in those values to find c
and you are done!
Good
Fantastic
To find the equation of a line parallel to the given line and passing through a point on the x-axis, we need to follow these steps:
1. Determine the slope of the given line.
2. Use the slope to find the slope of the parallel line.
3. Find the y-intercept of the parallel line using the given x-intercept.
4. Write the equation of the parallel line in slope-intercept form.
Let's go through these steps one by one:
1. The given line is 5x + 4y = 18. To find the slope, we need to rearrange the equation into the slope-intercept form (y = mx + b), where m represents the slope.
Starting with the given equation: 5x + 4y = 18
Rearrange the equation to solve for y: 4y = -5x + 18
Divide both sides by 4: y = (-5/4)x + 18/4
Simplify further: y = (-5/4)x + 9/2
Therefore, the slope of the given line is -5/4.
2. Since the line we want is parallel, its slope will be the same as the given line. Therefore, the slope of the parallel line is also -5/4.
3. We know that the parallel line passes through an x-intercept of 2 units. The x-intercept represents the point (x, 0). In this case, it is (2, 0).
4. Now, let's use the slope-intercept form (y = mx + b) and substitute the values we have:
y = (-5/4)x + b
Since the line passes through (2, 0), we can substitute these values into the equation:
0 = (-5/4)(2) + b
0 = -10/4 + b
Simplify: 0 = -5/2 + b
Add 5/2 to both sides: 5/2 = b
Therefore, the y-intercept of the line parallel to 5x + 4y = 18 and passing through the x-intercept of 2 units is 5/2.
The equation of the line is y = (-5/4)x + 5/2.