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4 years ago

Indicate the equation of the given line in standard form. The line through (2, -1) and parallel to a line with slope of 3/4

1 answer:

7 0

Well, for a line with a slope of 3/4, any other parallel line to it, will also have the same slope of 3/4

so if the line through (2, -1) is parallel to it, it has a slope of 3/4 as well

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 

\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{4}
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad 
\begin{array}{llll}
\textit{plug in the values for }
\begin{cases}
y_1=-1\\
x_1=2\\
m=\frac{3}{4}
\end{cases}\\
\textit{and move everything}\\
\textit{to the left-hand-side}
\end{array}\\

\left. \qquad \right. \uparrow\\
\textit{point-slope form}$

You might be interested in

a 9ft ladder is placed 4.5 feet from the base of a wall. How high up will the ladder reach? Round to the nearest hundredth.

spin [16.1K]

Answer:

$\huge\boxed{7.79 \ \text{feet}}$

Step-by-step explanation:

We know that we have a 9 foot long ladder resting upon a wall, with an unknown height, but the ladder is 4.5 feet away from the wall.

This can be represented as a triangle, where x is the unknown side.

| \

x | \ 9

| \

|_____\

4.5

We can use The Pythagorean Theorem to find the value of x. The theorem states that $a^2+b^2=c^2$ , where a and b are the lengths of the legs and c is the length of the hypotenuse.

However, we already know the hypotenuse and one leg. Therefore we can substitute inside the equation to find the missing value.

$a^2 + 4.5^2 = 9^2\\\\a^2 + 20.25 = 81\\\\a^2 = 60.75\\\\a \approx 7.79$

Hope this helped!

7 0

3 years ago

Find the missing coordinate to complete the ordered-pair solution to the given linear equation: A) y+6x=5 (a) (-1,?)

N76 [4]

A
a) y+6x=5 if x= -1 then y+6(-1)=5 then y = 11
b) same thing if x = 3 then y+6(3)=5 y+18=5 subtract both sides by -18 and leave y on left then add 5+(-18)= 13 then y=13

B same as above
question (a) asks you to solve for y because x is -2
(b) asks you to solve for x because y is known
3x+2y=-6 if y = 3 you write 3x+2(3)=-6 3x+6=-6 move the +6 over to right side by subtracting 6 from both side 3x=-6 + -6 so 3x=-12 to get rid of the 3 and only leave the x you want to divide both side by 3 then x= -12/3 then the answer would be x=-4

4 0

3 years ago

Read 2 more answers

What is the minimum value for g(x)=x^2-10x+16? Enter your answer in the box.

Anna71 [15]

Answer:

- 9

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - 10x

g(x) = x² - 10x + (- 5)² - (- 5)² + 16

= x² - 10x + 25 - 25 + 16

= (x - 5)² - 9 ← in vertex form

vertex = (5, - 9), hence

minimum value = - 9

6 0

4 years ago

The owner of a rental company rents bicycles and tricycles and keeps inventory by counting seats and wheels. One day, he counts

My name is Ann [436]

Answer:

2b + 3t = 60

Step-by-step explanation:

2b is the number of wheels on a bicycle

3t is the number of wheels on a tricycle

and 60 is the total number of wheels

5 0

3 years ago

Solve. M/9 = 8 A m = 1.1 B m = 17 C m = 27 D m = 72

Eddi Din [679]

Answer:

D. m=72

Step-by-step explanation:

M/9=8
To get rid of the 9, you have to multiply both sides by 9
M/9 ×9=8×9
M=8×9
8×9=72
M=72

3 0

3 years ago