write an equation of a line that has the same slope as 2x-5y=12 and the same y-intercept as 4y+24=5x.
The slope of the first line, which can be most easily seen when rewritten as
y = (2/5) x -12/5, is m = 2/5
The y-intercept of the second equation is what you get when x = 0. That number is y = -6
Therefore the equation of the line you want is
y = (2/5)x -6
To find the equation of a line with the same slope as 2x - 5y = 12, we need to rearrange the equation into slope-intercept form.
Step 1: Convert the equation to slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
2x - 5y = 12
-5y = -2x + 12
y = (2/5)x - (12/5)
From the equation, we can identify that the slope (m) is 2/5.
Step 2: Find the y-intercept using the equation 4y + 24 = 5x, which is already in slope-intercept form.
4y + 24 = 5x
4y = 5x - 24
y = (5/4)x - 6
From the equation, we can identify that the y-intercept (b) is -6.
Step 3: Write the equation of a line with the same slope and y-intercept.
Using the slope (m = 2/5) and the y-intercept (b = -6), the equation of the line is:
y = (2/5)x - 6
To find the equation of a line with the same slope as 2x - 5y = 12, we need to rearrange the given equation into slope-intercept form, which has the form y = mx + b, where m represents the slope, and b represents the y-intercept.
Step 1: Rearrange 2x - 5y = 12
First, we isolate y by subtracting 2x from both sides:
-5y = -2x + 12
Next, divide the entire equation by -5 to solve for y:
y = (2/5)x - (12/5)
Therefore, the equation 2x - 5y = 12 is equivalent to y = (2/5)x - (12/5), where the slope (m) is 2/5.
Now, let's find the y-intercept of the equation 4y + 24 = 5x. To do this, we need to isolate y.
Step 2: Rearrange 4y + 24 = 5x
First, subtract 24 from both sides to isolate 4y:
4y = 5x - 24
Next, divide the entire equation by 4 to solve for y:
y = (5/4)x - 6
So, the equation 4y + 24 = 5x is equivalent to y = (5/4)x - 6, where the y-intercept (b) is -6.
Now that we have the desired slope (2/5) and the y-intercept (-6), we can form the equation of the line.
Step 3: Write the equation with the given slope and y-intercept
Using the slope-intercept form y = mx + b, we substitute the values of m and b:
y = (2/5)x - 6
Therefore, the equation of the line with the same slope as 2x - 5y = 12 and the same y-intercept as 4y + 24 = 5x is y = (2/5)x - 6.