Write the equation of a line whose slope is the same as the line 3y-2x-10=0 and whose y-intercept is the same as the line 5x+3y=15
y = (2/3)x + 5
To find the equation of a line with the same slope as the line 3y - 2x - 10 = 0, we need to first rewrite the given equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's start with the first line:
3y - 2x - 10 = 0
First, isolate the y-term:
3y = 2x + 10
Divide every term by 3:
y = (2/3)x + 10/3
Therefore, the slope of the first line is 2/3.
To find another line with the same slope, we'll look at a second line: 5x + 3y = 15.
To rewrite this equation in slope-intercept form, isolate the y-term:
3y = -5x + 15
Divide every term by 3:
y = (-5/3)x + 5
The y-intercept of this line is 5.
So, the equation of the line with the same slope and y-intercept as the given lines is: y = (2/3)x + 5
To write the equation of a line with a specific slope and y-intercept, we can use the slope-intercept form of a linear equation which is:
y = mx + b
Where:
m represents the slope of the line
b represents the y-intercept of the line
Let's find the slope (m) and y-intercept (b) values separately:
1. Finding the slope:
The given line 3y - 2x - 10 = 0 can be rearranged into the standard form (y = mx + b):
3y - 2x - 10 = 0
3y = 2x + 10
y = (2/3)x + 10/3
Comparing this equation to the slope-intercept form (y = mx + b), we can determine that the slope (m) is 2/3.
2. Finding the y-intercept:
The other given line 5x + 3y = 15 is already in standard form, so we can directly identify the y-intercept (b) by rearranging it:
5x + 3y = 15
3y = -5x + 15
y = (-5/3)x + 5
Comparing this equation to the slope-intercept form, we can determine that the y-intercept (b) is 5.
Now that we have the slope (m = 2/3) and the y-intercept (b = 5), we can write the equation of the line:
y = (2/3)x + 5