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2 years ago

Find the y-intercept of a line parallel to 8x – 2y = 12 and passes through the point (5, 3).

Mathematics

1 answer:

Dmitry_Shevchenko [17]2 years ago

7 0

Answer:

-17

Step-by-step explanation:

8x -2y= 12

Divide the whole equation by 2:

4x -y= 6

Rewrite the equation into the slope-intercept form (y=mx+c, where m is the gradient while c is the y-intercept).

-y= -4x +6

y= 4x -6

Thus, gradient of given line= 4.

Since parallel lines have the same gradient, gradient of line= 4.

y= 4x +c

To find the y-intercept of the lone, substitute a pair of coordinates.

When x=5, y=3,

3= 4(5) +c

3= 20 +c

c= 3 -20

c= -17

Thus, the y-intercept of the line is -17.

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Find the slope of each line and then determine if the lines are parallel, perpendicular or neither. If a value is not an integer

Aleonysh [2.5K]

As given by the question

There are given that the point of two-line

$\begin{gathered} (1,\text{ 7) and (5, 5)} \\ (-1,\text{ -3) and (1, 1)} \end{gathered}$

Now,

From the condition of a parallel and perpendicular line

If the slopes are equal then the lines are parallel

If the slopes are negative reciprocal then the lines are perpendicular

If the slopes are neither of the above are true then lines are neither

Then,

First, find the slope of both of line

So,

For first-line, from the formula of slope

$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{5_{}-7_{}}{5_{}-1_{}} \\ m_1=-\frac{2}{4} \\ m_1=-\frac{1}{2} \end{gathered}$

Now,

For second-line,

$\begin{gathered} m_1=\frac{y_2-y_1}{x_2-x_1} \\ m_1=\frac{1_{}-(-3)_{}}{1-(-1)_{}} \\ m_1=\frac{4}{2} \\ m_1=2 \end{gathered}$

The given result of the slope is negative reciprocal because

$\begin{gathered} -\frac{1}{2}=-(-\frac{2}{1}) \\ -\frac{1}{2}=2 \end{gathered}$

Hence, the slope of line1 is -1/2, and slope of line2 is 2 and the lines are perpendicular.

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1 year ago

Rewrite each fraction in simplest form using the GCF of the numerator and denominator.

Elanso [62]

Answer:

$\sf 6. \quad \dfrac{7}{10}$

$\sf 7. \quad \dfrac{5}{17}$

Step-by-step explanation:

<h3>Question 6</h3>

To find the greatest common factor (GCF), first list the prime factors of each number:

42 = 2 × 3 × 7
60 = 2 × 2 × 3 × 5

42 and 60 share one 2 and one 3 in common.

Multiply them together to get the GCF: 2 × 3 = 6.

Therefore, 6 is the GCF of 42 and 60.

Divide the numerator and the denominator by the found GCF:

$\implies \sf \dfrac{42 \div 6}{60 \div 6}=\dfrac{7}{10}$

<h3>Question 7</h3>

To find the greatest common factor (GCF), first list the prime factors of each number:

80 = 2 × 2 × 2 × 2 × 5
272 = 2 × 2 × 2 × 2 × 17

80 and 272 share four 2s in common.

Multiply them together to get the GCF: 2 × 2 × 2 × 2 = 16.

Therefore, 16 is the GCF of 80 and 272.

Divide the numerator and the denominator by the found GCF:

$\implies \sf \dfrac{80 \div 16}{272 \div 16}=\dfrac{5}{17}$

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