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dusya [7]
1 year ago
6

2. What is the equation in slope-intercept form of the line that passes through thepoints (-4, 47) and (2, -16)?O21 979y=-2*+ 21

Oy=--Źx+97921Oy=-4x+5y=-21*+5--CLEAR ALL
Mathematics
1 answer:
trapecia [35]1 year ago
8 0

hello

the points given are (-4, 47) and (2, -16)

let's find the intercept of this equation

\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ x_2=2 \\ y_2=-16 \\ y_1=47 \\ x_1=-4 \end{gathered}\begin{gathered} m=\frac{-16-47}{2-(-4)} \\ m=-\frac{21}{2} \\ slope=-\frac{21}{2} \end{gathered}

now, since we know the value of the slope, we can use that in the standard equation on a straight line

the standard equation of a straight line is given as

\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}

we can pick any of the points and solve for intercept

let's use (2, -16)

\begin{gathered} x=2 \\ y=-16 \\ y=mx+c \\ m=-\frac{21}{2} \\ -16=-\frac{21}{2}(2)+c \\ -16=-21+c \\ \text{collect like terms} \\ c=-16+21 \\ c=5 \end{gathered}

now we know the value of intercept (c) = 5 and the slope (m) = 21/2

let's use this to write equation of the straight line

\begin{gathered} y=mx+c \\ y=-\frac{21}{2}x+5 \end{gathered}

from the calculations above, the equation of the straight line is given as y = -21/2x + 5

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Answer:

a) (11/7, 9/7)

b) There's no point of intersection

Step-by-step explanation:

a) x - 2y + 1 = 0

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Now we substitute x in the second equation:

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Now we substitute y in our first equation.

x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7.

The point of intersection is (11/7, 9/7)

b) x -2y +11 =0

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x-2y+11=0\\x=2y-11

-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2

Since this system of equations doesn't have a solution, the system has no point of intersection.

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DENIUS [597]

Answer:

4!

Step-by-step explanation:

Given four numbers 2, 4, 6, 8.

The numbers can be arranged to form an odd number which is less than 300.

That means we have three spaces to fill this. We can try out the different combination of the numbers.

Note that the numbers should be odd. So, in the unit digit should only be 5. 2, 4, 8 would make the number even.

Also, the first digit can only be two because other numbers would make it bigger than 300.

So, 2 ___ 5 is fixed. The middle digit could be any of the four.

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