The table shows the height of a plant as it grows. Which equation in point-slope form gives the plant’s height at any time? Time (months) Plant Height (cm) 3 21 5 35 7 49 9 63 (1 point) Responses y – 21 = (x – 3) y – 21 = Image with alt text: 7 over 2 ( x – 3) y – 21 = 7(x – 3) y – 21 = 7( x – 3) y – 3 = (x – 21) y – 3 = Image with alt text: 7 over 2 ( x – 21) The relationship is nonlinear.
To find the equation in point-slope form that represents the relationship between the time (months) and the plant's height (cm), we need to find the slope and a point on the line.
We can calculate the slope using two points: (3, 21) and (9, 63). The formula for the slope is (change in y)/(change in x), which gives us:
slope = (63 - 21)/(9 - 3) = 42/6 = 7
Now that we have the slope, we can use the point-slope formula, which is y - y1 = m(x - x1). Let's choose the point (3, 21) as our point on the line:
y - 21 = 7(x - 3)
Thus, the equation in point-slope form that represents the plant's height at any time is:
y - 21 = 7(x - 3)
To find the equation in point-slope form, we need to determine the slope and a point on the line.
To find the slope, we can choose any two points from the table. Let's choose the points (3, 21) and (9, 63). The formula for slope is given by:
slope = (change in y) / (change in x)
Using the values from the points, we get:
slope = (63 - 21) / (9 - 3)
= 42/6
= 7
Now, let's use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. We just found the slope, so we need to find the y-intercept.
To find the y-intercept, we can choose any point from the table. Let's choose the point (3, 21). Plugging in the values into the equation, we have:
21 = 7(3) + b
21 = 21 + b
b = 0
We found that the y-intercept, b, is 0.
Thus, the equation in point-slope form is:
y - 0 = 7(x - 3)
Simplifying, we have:
y = 7(x - 3)