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)3 215 357 49 9 63(1 point)Responses – 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.
Based on the given table, the relationship between time (months) and plant height (cm) is linear. We can find the equation using the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is any point on the line and m is the slope of the line. Let's take the point (3, 21) on the line.
So, the equation in point-slope form would be:
y - 21 = m(x - 3)
Now, let's calculate the slope (m) using another point on the line, for example, (5, 35):
m = change in y / change in x
= (35 - 21) / (5 - 3)
= 14 / 2
= 7
Plugging this value of m into the equation, we get:
y - 21 = 7(x - 3)
So, the correct equation in point-slope form is:
y - 21 = 7(x - 3)