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Lelechka [254]
3 years ago
15

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

Mathematics
1 answer:
Ket [755]3 years ago
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}
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Work out an equation of the straight line with gradient 3 that passes through the point with coordinates (2, 4).
Gnom [1K]

Answer:

The answer is

\huge \boxed{y = 3x - 10}

Step-by-step explanation:

To find an equation of a line given the slope and a point we use the formula

y -  y_1 = m(x -  x_1)

where

m is the slope

( x1 , y1) is the point

From the question the point is (2, 4) and the slope is 3

The equation of the line is

y - 4 = 3(x - 2) \\ y + 4 = 3x - 6 \\ y = 3x - 6 - 4

We have the final answer as

y = 3x - 10

Hope this helps you

3 0
3 years ago
Find the measure for angle f<br><br> 46<br> 34<br> 122<br> 58
xxMikexx [17]

Answer:

\angle f = 122\degree

Step-by-step explanation:

\angle d = 58\degree (vertical angles)

\angle f+\angle d= 180\degree

(Interior angles on the same side of transversal)

\angle f+ 58\degree = 180\degree

\angle f = 180\degree-58\degree

\huge \orange {\boxed {\angle f = 122\degree}}

5 0
3 years ago
Please, please, please, please help
Alexeev081 [22]

Answer:

27

Step-by-step explanation:

6 0
2 years ago
In the ratio 3:7 Zoe received £24 how much did Hannah receive last week
Ludmilka [50]
<span>ratio 3:7

Zoe received £24 (3 x 8 = 24)

</span>Hannah 7 x 8 = £56
3 0
3 years ago
Myra is a scientist and needs 45 gallons of a 16% acid solution. The lab is currently stocked only with a 20% acid solution and
asambeis [7]

Answer:

The volume of the solution with 20% acid is 27 gallons and the one with 10% acid is 18 gallons

Step-by-step explanation:

Myra needs to mix "x" gallons of the solution with 20% and "y" gallons of the solution with 10%. The volume of the final solution must be 45 gallons, therefore:

x + y = 45

The concentration of acid of the final solution is:

0.2*x + 0.1*y = 45*0.16

0.2*x + 0.1*y = 7.2

Therefore we have a system of equation:

x + y = 45

0.2*x + 0.1*y = 7.2

We need to multiply the first equation by -0.1:

-0.1*x -0.1*y = -4.5

0.2*x + 0.1*y = 7.2

We now sum both equation:

0.1*x = 2.7

x = 2.7/0.1 = 27 gallons

y = 45 - 27  = 18 gallons

6 0
3 years ago
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