A line is parallel to 5x+2y-8=0 and has the same y-intercept as x+4y-12=0
Find an equation for the line.
5x+2y-8=0
2y=-5x+8 Divide with 2
y=(-5/2)x+4
Slope is dy/dx
dy/dx=-5/2
x+4y-12=0 for x=0
4y-12=0
4y=12 Divide with 4
y=3 y-intercept
Line equation:
y = mx + b
This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.
m-5/2 b=3
Euation for the your line:
y=(-5/2)x+3
Type Feller:
m-5/2 b=3
Correct:
m=-5/2 b=3
To find the equation of the line that is parallel to the given line and has the same y-intercept as the second equation, we need to find the slope-intercept form of both lines.
The given line is 5x + 2y - 8 = 0. To find its slope-intercept form, we need to solve for y:
2y = -5x + 8
y = (-5/2)x + 4
So, the slope of the given line is -5/2.
The second equation is x + 4y - 12 = 0. To find its y-intercept, we need to set x to 0 and solve for y:
0 + 4y - 12 = 0
4y = 12
y = 3
So, the y-intercept of the second equation is 3.
Since the line we're looking for is parallel to the given line, it will have the same slope, which is -5/2. And since it has the same y-intercept as the second equation, which is 3, the equation of the line can be written as:
y = (-5/2)x + 3
To find an equation for a line that is parallel to the given line and has the same y-intercept as the given line, we need to follow these steps:
Step 1: Convert the given lines into slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
Given line 1: 5x + 2y - 8 = 0
Rearrange the equation to isolate y:
2y = -5x + 8
Divide both sides by 2:
y = -5/2x + 4
Given line 2: x + 4y - 12 = 0
Rearrange the equation to isolate y:
4y = -x + 12
Divide both sides by 4:
y = -1/4x + 3
Step 2: Identify the slope (m) of the given line. For parallel lines, the slope remains the same.
The slope of the given line is -5/2.
Step 3: Identify the y-intercept (b) of the given line. The required line should have the same y-intercept.
The y-intercept of the given line is 4.
Step 4: Use the slope and y-intercept to form the equation of the line.
The equation of the required line will have the same slope (-5/2) as the given line and the same y-intercept (4) as the given line.
Therefore, the equation for the line parallel to 5x + 2y - 8 = 0 and the same y-intercept as x + 4y - 12 = 0 is:
y = -5/2x + 4