Mathematics: (a) derive an equation of the line passing through the points a(0, 545) and b(4, 726). (let t be the independent variable and y be the dependent variable.)

(a) derive an equation of the line passing through

Ответ:

sugeilochoa

02.01.2022

Mathematics

The equation of the line is y=45.25t+545

Step-by-step explanation:

The general for of a line is:

y=mt+n (1)

where:

is the slope of the line and is the intercept with the axis of the dependent variable, in this case.

In order to obtain the value of the slope () we can use the corresponding slope formula:

$m=\frac{y_{2}-y_1 }{t_2-t_1}$ (2)

where t_1, t_2, y_1 and y_2 are the corresponding coordinates of the given points. In this case:

$t_1=0\\t_2=4\\y_1=545\\y_2=726\\$

Substituting these values in equation (2) we obtain:

$m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25$

Hence, the line equation is now:

y=45.25t+n (3)

Now to obtain the value of you can follow two options:

You can substitute one of your points,

, in equation (3). In this way, you will obtain an equation where the variable is

Note that for this question, it is easier to select point A because of having the independent variable equals to zero t=0 . Hence, substituting point A in equation (3):

$45.25*0+n=545\\n=545$

Therefore, the line equation is: y=45.25t+545

The second option to find is to think of the meaning of the intercept. The intercept of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that is equal to 545 .

See the attachment for a plot of the line.

(a) derive an equation of the line passing through the points a(0, 545) and b(4, 726). (let t be the

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(a) derive an equation of the line passing through the points a(0, 545) and b(4, 726). (let t be the independent variable and y be the dependent variable.)

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