Answer:
To find a line with the same slope as the equation 6y + 10 = 3x and the same y-intercept as the equation 4x - 3y = 9, we need to determine the slope and y-intercept of each equation separately.
Let's start by rearranging the first equation, 6y + 10 = 3x, into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Subtracting 10 from both sides of the equation gives us:
6y = 3x - 10
Dividing both sides by 6, we get:
y = (3/6)x - (10/6)
Simplifying further:
y = (1/2)x - (5/3)
From this equation, we can see that the slope is 1/2 and the y-intercept is -5/3.
Now let's rearrange the second equation, 4x - 3y = 9, into slope-intercept form.
Subtracting 4x from both sides of the equation gives us:
-3y = -4x + 9
Dividing both sides by -3, we get:
y = (4/3)x - (9/3)
Simplifying further:
y = (4/3)x - 3
From this equation, we can see that the slope is 4/3 and the y-intercept is -3.
To find a line with the same slope as the first equation and the same y-intercept as the second equation, we can use these values to construct our desired line.
The slope of our desired line will be 1/2, and the y-intercept will be -3. Therefore, our final equation will be in the form:
y = (1/2)x - 3
This equation represents a line that has the same slope as 6y + 10 = 3x and the same y-intercept as 4x - 3y = 9.
In summary, the line that has the same slope as 6y + 10 = 3x and the same y-intercept as 4x - 3y = 9 is given by the equation y = (1/2)x - 3.
Explanation: