A line (L) has a y intercept of (0,4) and is parallel to a line (A) with the equation y=3x + 6. Write the equation for line (L) in slope intercept form
The slope-intercept form of the equation of a line is: y = mx + b, where m is the slope and b is the y-intercept. Hence, we need to know these two parameters to know the equation of the line.
line (L) passes through the point (0,4). Hence, it's y-intercept is 4 -- that is, b = 4.
We know that line (L) is parallel to line (A). Two lines are parallel if and only if they have the same slope. Hence, the slope of L is the same as the slope of A. A has equation y = 3x + 6, which means that its slope is 3, and hence this is also the slope of L -- that is, m = 3.
Now, we now that for L, m = 3, and b = 4. We simply substitute this to the equation to get the equation of L:
y = 3x + 4
If a line is parallel to another line, the two lines will have the same slope. Therefore, if the new line, line, line L is to be parallel to line A it must have a slope of 3.
Line A is written in slope-intercept form: `y=mx+b` which tells us m is the slope and b is the y-intercept.
So, the slope of the line has to be 3 and the y-intercept given is (0, 4),
therefore the equation of line L is `y=3x + 4.`