a bamboo plant is growing 1 foot per day. when you first measure it, it is 4 feet tall.
a. write an equation to describe the height y, in feet, of the bamboo plant x days after you measure it.
would it be: x+y=4?
b. what is the y intercept?
would it be: x+y=4?
This is clearly this not correct if you put numbers into the equation. If y is the height after 10 days then the height is the plant is
10+y=4
so y=-6 or 6ft below ground!
The correct equation is
y=4+x
where both y and x are in feet. This agrees with the description as at time zero, x=0, the y=4 i.e 4ft. After 10 days the plant will be
y=4+10 = 14 or 14 ft tall. Which is a sensible value.
If we compare the equation with the general equation for a straight line which is
y=mx+c
where
m=gradient and
c=the y intercept
we see that m=1 and
c=4 (or the line passes through (0,4)
a. The correct equation to describe the height y, in feet, of the bamboo plant x days after you measure it is:
y = 4 + x
b. The y-intercept is the value of y when x is 0. In this case, when you first measure the bamboo plant, it is already 4 feet tall, so the y-intercept is 4.
a. To write an equation to describe the height y, in feet, of the bamboo plant x days after you measure it, you can use the formula: y = mx + b, where y represents the height, x represents the number of days, m represents the rate of growth (1 foot per day in this case), and b represents the initial height (4 feet in this case). Therefore, the equation would be: y = 1x + 4, which simplifies to y = x + 4.
b. The y-intercept is the value of y when x is equal to 0. In this case, the initial height of the bamboo plant when you first measure it is 4 feet. So, the y-intercept would be 4.