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Can you help me find the slope, y-intercept, and the equation based off this chart?

Can you help me find the slope, y-intercept, and the equation based off this chart-example-1
User DockYard
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1 Answer

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y-interceptis As given by the question

There are given that the value of x and y.

Now,

For finding the value of the slope, choose two-point from the given table

So,

Suppose the two points are:


(1,\text{ 5) and (}3,\text{ 3)}

Now,

From the formula of slope:


m=(y_2-y_1)/(x_2-x_1)

Where,


x_1=1,y_1=5,x_2=3,y_2=3

Put all the above value into the given formula

So,


\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=\frac{3_{}-5_{}}{3_{}-1_{}} \\ m=-(2)/(2) \\ m=-1 \end{gathered}

Hence, the value of the slope is -1.

Now,

For the equation of the line that is based on the given chart, use two supposes point and the given slope.

So,

The two poin and slope is:


(1,\text{ 5) and (3, 3) and m=-1}

Then,

From the formula of two point form;


(y-y_1)=m(x-x_1)

Where,


x_1=1,y_1=5,x_2=3,y_2=3,\text{ m=-1}

Then,

Put all the given value into the above formula

So,


\begin{gathered} (y-y_1)=m(x-x_1) \\ (y-5_{})=-1(x-1_{}) \\ (y-5)=-x+1 \\ y-5+x-1=0 \\ y+x-6=0 \end{gathered}

Hence, the equation of the line is:


y=-x+6

Now,

To find the y-intercept, put x=0 and solve for x

So,

The y intercept of the given equation is:


\begin{gathered} y=-x+6 \\ y=-(0)+6 \\ y=6 \end{gathered}

Hence, the y-intercept is (0, 6)

User Waxhaw
by
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