Question

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

Answer 1

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)