Question

read the instructions first and answer the questions help my sister's homework​

Answer 1

Method to find the trend of linear equation:-

☆Let the linear equation be y = mx + c,

where, m is slope and c is intercept on y - axis.

• A positive slope means that as a line on the line graph moves from left to right, the line rises. It shows a positive trend.

• A negative slope means that as a line on the line graph moves from right to left, the line falls. it shows a negative trend.

• A slope of zero means that there is a constant relationship between x and y. Graphically, the line is flat; the rise over run is zero. There is no trend.

• A slope undefined means that there is again constant relationship between x and y. Graphically the line is vertical. The run over rise is zero. There is no trend.

$\bf \:\large \red{AηsωeR : 1.} ✍$

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

$\bf \:❶ \: y = - \dfrac{3}{5} x + 4$

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf 5 & \sf 1 \\ \\ \sf 0 & \sf 4 \end{array}} \\ \end{gathered}$

↝ For graph see the first attachment.

On comparing line (1) with y = mx + c, we get

$\bf \:m = - \dfrac{3}{5}$

Since, slope is negative, therefore the line has negative trend.

━─━─━─━─━─━─━─━─━─━─━─━─━

$\bf \:\large \red{AηsωeR : 2.} ✍$

$\bf \:The \: equation \: is \: y = - \: 9$

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf 1 & \sf - 9 \\ \\ \sf 0 & \sf - 9 \end{array}} \\ \end{gathered}$

↝ For graph see the second attachment.

On comparing the line with y = mx + c, we get m = 0.

It means, there is no trend.

━─━─━─━─━─━─━─━─━─━─━─━─━

$\bf \:\large \red{AηsωeR : 3.} ✍$

$\bf \:The \: equation \: is \: y =4x - \dfrac{3}{2}$

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf 1 & \sf 2.5 \\ \\ \sf 0 & \sf - 1.5 \end{array}} \\ \end{gathered}$

↝ For graph see the third attachment.

On comparing the line with y = mx + c, we get m = 4.

It means there is positive trend.

━─━─━─━─━─━─━─━─━─━─━─━─━

$\bf \:\large \red{AηsωeR : 4.} ✍$

$\bf \:The \: equation \: is \: x = - 2$

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf - 2 & \sf 0 \\ \\ \sf - 2 & \sf 1 \end{array}} \\ \end{gathered}$

↝ For graph see the fourth attachment.

On comparing the line with y = mx + c, we get, m = not defined

It means there is no trend.

━─━─━─━─━─━─━─━─━─━─━─━─━

$\bf \:\large \red{AηsωeR : 5.} ✍$

$\bf \:The \: equation \: is \: 4x + y = 7$

can be rewritten as

$\bf\implies \:y = - 4x + 7$

First, we find coordinates of points, which are lies in the line, in both x-axis & y-axis, which represents the graph structure.

➣ To calculate the coordinates of points, which are lies on the line, are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{cccc}\bf x & \bf y \\ \frac{\qquad \qquad \qquad \qquad}{} & \frac{\qquad \qquad \qquad \qquad}{} \\ \sf 1 & \sf 3 \\ \\ \sf 0 & \sf 7 \end{array}} \\ \end{gathered}$

↝ For graph see the fifth attachment.

On comparing the line with y = mx + c, we get m = - 4.

It means there is negative trend.

━─━─━─━─━─━─━─━─━─━─━─━─━

Answer 2

Step-by-step explanation:

Given that:-

1.Given equation is y=-3/5 x+4

On comparing with y=mx+c

m=-3/5

Slope =-3/5

It is a negative number

The trend of the graph:-It moves from left to right. It falls down.

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2.Given equation is y=-9

It can be written as y=ox+(-9)

On comparing with y=mx+c

Slope(m)=0

Trend of the graph:

Slope is zero so It is Parallel to X-axis

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3.Given equation is y=4x-3/2

On comparing with y=mx+c

m=4

slope(m)=4

Trend of the graph:Slope of the given equation is a positive number and It movies from left to right and it falls raises

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4.Given equation is x=-2

Trend of the graph:The above equation shows Y axis

It is parallel to y-axis .that is the slope is not defined.

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5.Given equation is 4x+y=5

=>y=-4x+5

On comparing with y=mx+c

Slope=-4

It is a negative number

Trend of the graph: It moves from left to right sides. It falls down.

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