Question

Determine the linear equation from the graph below.
1 Height of a balloon
3
+
.
.
.
.
.
Height (1000 ft)
10 20 30 40 50 60
Time (sec)

Answer 1

Answer:  $y=\frac{1}{30}x+1$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

The slope of the line can be calculated with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Pick to  points of the given line. You can choose the point (60,3) and the point (30,2).

Then, substituting into the formula, you get:

 $m=\frac{2-3}{30-60}=\frac{1}{30}$

You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:

$b=1$

Substituting the slope and the y-intercept found into  $y=mx+b$, you get the equation of this line:

 $y=\frac{1}{30}x+1$

Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.

Answer 2

Answer:

The equation of the given line is :y = 0.04x + 0.6.

Step-by-step explanation:

From the given data , we can select two coordinates to determine the equation of the given line:

Let the point be $(10,1),(60,3)$

The equation of the line will be determined by the help of point slope form:

Slope of the line = $m=\frac{y_2-y_1}{x_2-x_1}$

$(y-y_1)=m(x-x_1)$

The equation of the line is :

$m=\frac{3-1}{60-10}=\frac{2}{50}=0.04$

$(y-1)=0.04(x-10)$

$y-1=0.04x-0.4$

$y=0.04x+0.6$

The equation of the given line is :y = 0.04x + 0.6.