Question

The table shows the height of a tree as it grows. What equation in slope-intercept form gives

Answer 1

Answer:

$y=4.5x+5$

Step-by-step explanation:

The slope of the line passing through the points $(x_1,y_1)$ and $(x_2,y_2)$ is

$\dfrac{y_2-y_1}{x_2-x_1}$

The line passes through the points (2,14) and (4,23), then its slope is

$\dfrac{23-14}{4-2}=\dfrac{9}{2}=4.5$

The equation of the line in slope-intercept form is

$y=mx+b,$

wher m is the slope and b is y-intercept.

Thus, the equation is

$y=4.5x+b$

This line passes through the point (2,14), its coordinates satisfy the equation, so

$14=4.5\cdot 2+b\\ \\9+b=14\\ \\b=14-9\\ \\b=5$

Hence, the equation is

$y=4.5x+5$