Find the slope of the line that passes through (10,4) and (7,9)

Mathematics

1 answer:

Mkey [24]1 year ago

4 0

I will take you the steps to obtain the slopes passing two points

step 1 : list the parameters

$\begin{gathered} \text{from (10, 4)} \\ x_1=10,y_1=\text{ 4} \\ \text{from (7,9)} \\ x_2_{}=7,y_2=\text{ 9} \end{gathered}$

step 2: Apply the equation to obtain the slope between two points

$\begin{gathered} \text{slope = }\frac{rise}{fall}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \Rightarrow\frac{9\text{ - 4}}{7\text{ - 10}}\text{ =}\frac{5}{-3} \\ \\ slope=-\frac{5}{3} \end{gathered}$

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A tub filled with 50 quarts of water empties at a rate of 2.5 quarts per minute. let w = quarts of water left in the tub and t =

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This is a linear relationship. The slope-intercept form of the linear equation is:

$y=mx+c$

Where,

m is the rate of change (positive if increasing rate and negative if decreasing rate)
c is the y intercept, or the initial value

Rate of change is 2.5 quarts per minute (it is decreasing so m is -2.5)

Initial value is 50 quarts, so c is 50.

Plugging in the values we get $y=-2.5x+50$ .

Changing variables to w instead of y and t instead of x, gives us,

$w=50-2.5t$ . Where w is warts of water left in the tub and t is the time in minutes.

There is no viable solution when t=30 because at t=20, w=0 ( $0=50-2.5(20)$ ). It means after 20 minutes, there is no water left. So t=30 minutes doesn't make sense.