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Mathematics, 29.10.2020 19:10 seoulux

A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?

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Answer from: flowergirly34

The value of k is 10.From the coordinate given (0, 10) and (4, 0), we can see that the y intercept and x intercept of the graph is 10 and 4 respectively

Given the line that passes through points (0, k) and (4,0) and has a slope of –2.5, we need to get the value of "k

The formula for calculating the slope of a line is expressed as:

$m=\frac{y_2-y_1}{x_2-x_1}\\-2.5 = \frac{0-k}{4-0}\\-2.5=\frac{-k}{4} \\Cross \ multiply\\-2.5 \times 4 = -k\\-10 = -k\\k = 10$

Hence the value of k is 10.

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From the coordinate given (0, 10) and (4, 0), we can see that the y intercept and x intercept of the graph is 10 and 4 respectively

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Answer from: leshayk91

A. The equation of the line is y=−2.5x+10.

C. The y-intercept is k.

F. The value of k is 10.

Step-by-step explanation:

A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?

A. The equation of the line is y=−2.5x+10.

B. The equation of the line is y=−2.5x.

C. The y-intercept is k.

D. The y-intercept is 4.

E. The value of k is 4.

F. The value of k is 10.

Solution:

The slope of a line is the ratio of the vertical change to the horizontal change. The slope (m) of a line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is:

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

Given that the line passes through (0, k) and (4,0)

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

$-2.5=\frac{0-k}{4-0}\\\\-2.5=\frac{-k}{4}\\\\k=10$

The equation of the line is given as:

$y-y_1=m(x-x_1)\\\\y-10=-2.5(x-0)\\\\y = -2.5x+10$

The y intercept is the value of y when x = 0, hence intercept = k

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Answer from: Quest

answer: 59

step-by-step explanation:

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Answer from: Quest

a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

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