Mathematics: Write the equation of the line parallel to 4y - x = -20 that passes through the point (8,3).

Write the equation of the line parallel to 4y

campbellkruger

08.08.2021

y= ¼x +1

Step-by-step explanation:

Rewriting the equation into the slope-intercept form (y= mx +c, where m is the gradient and c is the y- intercept):

4y -x= -20

4y= x -20 (+x on both sides)

y= ¼x -5 (÷4 throughout)

Thus, slope of given line is ¼.

Parallel lines have the same gradient.

Gradient of line= ¼

y= ¼x +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= 8, y= 3,

3= ¼(8) +c

3= 2 +c

c= 3 -2

c= 1

Hence the equation of the line is y= ¼x +1.

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Nathaliasmiles

01.04.2022

$x \approx 51.058\°$

or in radians

$x \approx 0.8911$

Step-by-step explanation:

We have the opposite side of angle x and hypotenuse of the right triangle.

$\text{sin}(\theta)= \frac{\text{opposite}}{\text{hypotenuse}}$

$\text{sin}(x)= \frac{14}{18}$

$\text{sin}(x)= \frac{7}{9}$

$x \approx 51.058\°$

Let's find the other side.

$18^2=14^2+b^2\\324=196+b^2\\b=\sqrt{128}$

$b=8\sqrt{2}$

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