I need an equation for L that satisfies the given geometric condition.
L has a y intercept (0,3) and is parallel to the equation y = 2/3x+1
Please take me step by step so I can understand.
Thank you
well they would have the same slope 2/3x
except this line has a y intercept of 1, not 3
so you put 3 in for 1 and you have you line
To find the equation for L that satisfies the given geometric condition, we need to use the fact that L is parallel to the equation y = (2/3)x+1.
Step 1: Understand the slope-intercept form of a linear equation
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Step 2: Determine the slope of the given equation
In the equation y = (2/3)x + 1, the coefficient of x (2/3) represents the slope. So the slope of the given equation is 2/3.
Step 3: Use the slope and the given y-intercept to find the equation for L
Since L is parallel to the given equation, it will have the same slope, 2/3. Additionally, L has a y-intercept of (0,3) instead of (0,1).
Plugging in the values into the slope-intercept form equation, we have:
y = (2/3)x + b
We know that L passes through the point (0,3). Thus, we can substitute x = 0 and y = 3 into the equation to find the value of b.
3 = (2/3)(0) + b
3 = 0 + b
b = 3
Step 4: Write the final equation for L
Now that we have the slope (2/3) and the y-intercept (3), we can substitute these values back into the slope-intercept form equation.
Therefore, the equation for L is:
y = (2/3)x + 3