Use the point slope equation to identify the slope and the coordinates of a point

Mathematics

2 answers:

Mekhanik [1.2K]3 years ago

7 0

Answer:

[1, 4]; 1 = m

Step-by-step explanation:

According to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so in this case, the coordinates are [1, 4]. Now, the rate of change [slope] is 1 because an invisible coefficient is always assumed to be 1.

I am joyous to assist you anytime.

nataly862011 [7]3 years ago

3 0

Answer:

The slope of the line is 1 and it passes through the point (1,4).

Step-by-step explanation:

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$ .... (1)

The given equation of line is

$y-4=(x-1)$ .... (2)

We need to find the slope and the coordinates of a point on the given line.

On comparing (1) and (2) we get

$m=1$

$x_1=1$

$y_1=4$

Therefore, the slope of the line is 1 and it passes through the point (1,4).

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PART A:
To obtain an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days, we use the fomula for the equation of a straight line.

Recall that the equation of a straight line passing through points $(x_1,\ y_1)$ and points $(x_2,\ y_2)$ is given by
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Given that Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.
This means that the lne modelling this situation crosses points (2, 125) and (5, 275).

The equation modelling the total rent (y) that Marguerite has to pay for renting the truck for x days is given by,
$\frac{y-125}{x-2} = \frac{275-125}{5-2} = \frac{150}{3} =50 \\ \\ y-125=50(x-2)=50x-100 \\ \\ y=50x+25$

Writing the equation in standard form, we have
50x - y = -25

PART B:
Writing the function using function notation means making 'y' the subject of the formula and then replacing the 'y' with 'f(x)'.

Recall that from part A, we have that the equation for the total rent (y) that Marguerite has to pay for renting the truck for x days is given by y = 50x + 25.

Writing the equation using the function notation, we have
f(x) = 50x + 25

PART C:
To graph the function, we label the x-axis 'number of days' and label the y-axis 'total rent'. the x-axis is numbered using the intervals of 1 while the y-axis is labelled using the intervals of 50.
The points (2, 125) and (5, 275) are marked on the coordinate axis and a straight line is drawn to pass through the two points.

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