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?
Without the table, it is not possible to determine the equation in point-slope form. The equation in point-slope form is expressed as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. The table is needed to determine the specific data points and slope in order to derive the equation.
To determine the equation in point-slope form, we need to find the slope (rate of growth) and a point on the table. Could you provide the table with the corresponding plant heights at different times?
To find the equation in point-slope form that gives the plant's height at any time, we need to identify two key pieces of information: a point on the line and its slope.
Based on the given table, we can select any two points to determine the slope. Let's pick two consecutive points: (time1, height1) and (time2, height2). The slope, m, can be calculated using the formula:
m = (height2 - height1) / (time2 - time1)
Now that we have the slope, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
In this equation, (x1, y1) represents a point on the line, and m represents the slope.
Let's use the point (time1, height1) as our point on the line. Plugging the values into the equation, we get:
height - height1 = m(time - time1)
Finally, rearranging the equation, we can rewrite it in point-slope form:
height = m(time - time1) + height1
Therefore, the equation in point-slope form that gives the plant's height at any time is:
height = m(time - time1) + height1, where m represents the slope and (time1, height1) represents a point on the line.