Write an equation of the line with a y-intercept of -4 that is parallel to 6x-2y=13
Um y=3x+(-4) right?
If two lines are parallel, then they have the same slope.
6x-2y =13
-2y = -6x +13
y = 3x -13/2
slope m= 3
y-intercept b=-4
y=mx +b
can you finish from here?
To find the equation of a line that is parallel to another line, we need to know that parallel lines have the same slope. First, let's find the slope of the line given by the equation 6x - 2y = 13.
To do this, we rearrange the equation in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation 6x - 2y = 13, we isolate y by subtracting 6x from both sides:
-2y = -6x + 13
Then, we divide both sides by -2:
y = (6/2)x - 13/(-2)
y = 3x + 13/2
From this, we can see that the slope of the line 6x - 2y = 13 is 3.
Now, since we want to find a line that is parallel to this line and has a y-intercept of -4, we know that the slope should also be 3. And we can use the point-slope form of a linear equation, y - y₁ = m(x - x₁), to find the equation of the line.
Using the given y-intercept of -4 as our y-coordinate (y₁), we have y - (-4) = 3(x - x₁), which simplifies to y + 4 = 3(x - x₁).
Since we want our line to be parallel to 6x - 2y = 13, we can choose any x-coordinate (x₁). Let's choose x = 0 for simplicity.
Substituting the values, we have y + 4 = 3(x - 0), which simplifies to y + 4 = 3x.
Therefore, the equation of the line with a y-intercept of -4 that is parallel to 6x - 2y = 13 is y + 4 = 3x.
To find the equation of a line that is parallel to a given line and has a specific y-intercept, we will use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
First, let's convert the given equation, 6x - 2y = 13, into slope-intercept form.
Starting with the equation:
6x - 2y = 13
We need to isolate y on one side.
Subtract 6x from both sides:
-2y = -6x + 13
Next, divide the entire equation by -2 to solve for y:
y = 3x - (13/2)
Now that we have the slope of the given line, which is 3, we know that any line parallel to this one will also have a slope of 3.
Since our new line has a y-intercept of -4, we can plug in the values we have into the slope-intercept form:
y = mx + b
Substitute m = 3 and b = -4:
y = 3x - 4
Therefore, the equation of the line with a y-intercept of -4 that is parallel to 6x - 2y = 13 is y = 3x - 4.