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Nana76 [90]
3 years ago
6

Find the slope and y intercept of the line represented by each table​

Mathematics
1 answer:
zvonat [6]3 years ago
7 0

Answer:

see explanation

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 )

Calculate m using the slope formula

(1)

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 22) and (x₂, y₂ ) = (4, 32) ← 2 ordered pairs from the table

m = \frac{32-22}{4-2} = \frac{10}{2} = 5, thus

y = 5x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (6, 42), then

42 = 30 + c ⇒ c = 42 - 30 = 12

Thus Table 1 has slope = 5 and y- intercept = 12

(2)

Using (x₁, y₁ ) = 2, 15) and (x₂, y₂ ) = (1,8) ← 2 ordered pairs from the table

m = \frac{8-15}{1-2} = \frac{-7}{-1} = 7, thus

y = 7x + c ← is the partial equation

To find c substitute (3, 22) into the partial equation

22 = 21 + c ⇒ c = 22- 21 = 1

Thus Table 2 has slope = 7 and y- intercept = 1

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Answer:

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Step-by-step explanation:

8:9

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Solve the equation using the quadratic formula : x^2-10x+25=18
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x^2-10x+25=18 \\ \\x^2-10x+25-18 = 0\\ \\ x^2-10x+ 7 =0 \\ \\a=1 , b = -10 , c= 7 \\ \\ \Delta = b^{2}-4ac = (-10)^{2}-4*1*7=100-28 = 72 \\ \\\sqrt{\Delta }=\sqrt{72}= \sqrt{2*36} =\sqrt{36}*\sqrt{2} =6\sqrt{2}

x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{10- 6\sqrt{2}}{2}=\frac{2(5-3\sqrt{2})}{2}= 5-3\sqrt{2}\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{10+ 6\sqrt{2}}{2}=\frac{2(5+3\sqrt{2})}{2}= 5+3\sqrt{2}


Answer : \ x= 5-3\sqrt{2} \ \ or \ \ x = 5+3\sqrt{2}


8 0
3 years ago
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