Write the slope-intercept form of the equation of the line described.

Mathematics

2 answers:

Romashka [77]2 years ago

6 0

Answer:

<h3>(4-4 = 0) - (4x5 =20) xDDddd</h3>

Sholpan [36]2 years ago

5 0

Answer:

$y = \frac{1}{4} x - 3$

Step-by-step explanation:

<u>Slope-intercept form:</u>

y= mx +c, where m is the gradient and c is the y-intercept.

The product of the gradients of perpendicular lines is -1.

-4m= -1

m= -1 ÷(-4)

m= ¼

Substitute m= ¼ into the equation:

y= ¼x +c

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

y= ¼x +c

When x= -4, y= -4,

-4= ¼( -4) +c

-4= -1 +c

c= -4 +1

c= -3

Thus, the equation of the line is y= ¼x -3.

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What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

EleoNora [17]

Check the picture below.

so... you can pretty much see how long RS and QT are, you can just count the units off the grid.

now, let's find QR's length

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Q&(~ 8 &,& 8~) 
% (c,d)
&R&(~ 14 &,& 16~)
\end{array}~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
QR=\sqrt{(14-8)^2+(16-8)^2}\implies QR=\sqrt{6^2+8^2}
\\\\\\
QR=\sqrt{36+64}\implies QR=\sqrt{100}\implies QR=10$

and let's also find the length for ST

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ 20 &,& 16~) 
% (c,d)
&T&(~ 22 &,& 8~)
\end{array}~ 
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
ST=\sqrt{(22-20)^2+(8-16)^2}\implies ST=\sqrt{2^2+(-8)^2}
\\\\\\
ST=\sqrt{4+64}\implies ST=\sqrt{68}\implies ST=\sqrt{4\cdot 17}
\\\\\\
ST=\sqrt{2^2\cdot 17}\implies ST=2\sqrt{17}$

so, add the lengths of all sides, and that's the perimeter of the trapezoid.