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svetlana [45]
2 years ago
8

The slope of the line that contains the points (4, 10) and (5, 13) is 3. Find the y-intercept.

Mathematics
1 answer:
AlekseyPX2 years ago
7 0

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using (4, 10 ) , then

10 = 12 + c ⇒ c = 10 - 12 = - 2 → B

D

Given m = 4 then

y = 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (3, 19 ), then

19 = 12 + c ⇒ c = 19 - 12 = 7 → D

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Solve for x, y, and z. <br> y=1/2z<br> x+2y+5z=2<br> 3x+6y-3z=9
Contact [7]
Rearrange the equation,

0x + y - ½z = 0 ==> Equation 1
x + 2y + 5z = 2 ==> Equation 2
3x + 6y - 3z = 9 ==> Equation 3

Put the 3 equation in matrix form,

0\ \ \ \ \ 1\ \ -{\frac{1}{2} }\ \ \ \ \ \ \ \ 0 \\ 1\ \ \ \ \ 2\ \ \ \ \ \ \ 5\ \ =\ 2 \\ 3\ \ \ \ \ 6\ \ -3\ \ \ \ \ \ \ \ \ 9

Find the determinant, D, of the matrix,

0\ \ \ \ \ 1\ \ -{\frac{1}{2} } \\ 1\ \ \ \ \ 2\ \ \ \ \ \ \ 5\ = \ D \\ 3\ \ \ \ \ 6\ \ -3

By Sarrus' rule,
D = [(0 × 2 × -3) + (1 × 5 × 3) + (-½ × 1 × 6)] - [(-½ × 2 × 3) + (5 × 6 × 0) + (-3 × 1 × 1)]
D = [0 + 15 + (-3)] - [(-3) + 0 + (-3)]
D = 12 + 6
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By cramer's rule,

x = Determinant of x ÷ D
Let determinant of x = Dx,

0\ \ \ \ \ 1\ \ -{\frac{1}{2} } \\ 2\ \ \ \ \ 2\ \ \ \ \ \ \ 5\ = \ Dx \\ 9\ \ \ \ \ 6\ \ -3
To get this determinant, substitude 0, 2 and 9 with the unknown you're finding, in this case, x.

By Sarrus' rule,
Dx = [(0 × 2 × -3) + (1 × 5 × 9) + (-½ × 2 × 6)] - [(-½ × 2 × 9) + (0 × 5 × 6) + (-3 × 1 × 2)]
Dx = [0 + 45 + (-6)] - [-9 + 0 + (-6)]
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x = Dx ÷ D
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By cramer's rule,

y = Determinant of y ÷ D
Let determinant of y = Dy

0\ \ \ \ \ 0\ \ -{\frac{1}{2} } \\ 1\ \ \ \ \ 2\ \ \ \ \ \ \ 5\ = \ Dy \\ 3\ \ \ \ \ 9\ \ -3

By Sarrus' rule,
Dy = [(0 × 2 × -3) + (0 × 5 × 3) + (-½ × 1 × 9)] - [(-½ × 2 × 3) + (5 × 9 × 0) + (-3 × 0 × 1)
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Dy = -4½ + 3
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y = Dy ÷ D
y = -1½ ÷ 18
y ≈ 0.0833 (3 significant figure)

Solving z using equation rule,
y = ½z
0.0833 = ½z
z = 0.0833 ÷ ½
z ≈ 0.167 (3 significant figure)

∴ x = 3, y = 0.0833 and z = 0.167.
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