Question

Use graph to find the slope and y-intercept of the line. Compare the values to the equation y= -x+5

Answer 1

As given by the question

There are given that the graph of the line.

Now,

To find the slope and y-intercept of the line, first select two intersect point from the graph.

Then,

The points are:

`(0,\text{ 5) and (5, 0)}`

Then,

First find the slope,

So,

From the formula of slope,

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

Where,

`x_1=0,y_1=5,x_2=5,y_2=0`

Then,

Put all the value into the given formula.

So,

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=\frac{0_{}-5_{}}{5_{}-0_{}} \\ m=-(5)/(5) \\ m=-1 \end{gathered}`

Now,

From the standard form of the line,

`y=mx+b`

Then,

Put y is 5, x is 0 and m is -5 into the above equation to find the y-intercept

So,

`\begin{gathered} y=mx+b \\ 5=-1(0)+b \\ b=5 \end{gathered}`

Hence, the value of the y-intercept is 5.

Now,

The line equation is shown below:

`\begin{gathered} y=mx+b \\ y=-1x+b \\ y=-x+5 \end{gathered}`

Hence, the slope of the line is -1, y-intercept of the line is 5 and the equation of line is y = -x + 5.