Question

Need help on this Picture below Thanks .

Answer 1

See below

Explanation:

Part A

We are given that a line contains the points (0,5) and (4,1). We want to graph this line on the point.

First, we need to put the 2 points on the line.

(0,5) has an x value of 0 and a y value of 5.

(4,1) has an x value of 4 and a y value of 1.

Then, draw a line through those two points.

See the attachment below for the graph!

Part B

We want to find the slope (m) of the line.

We can use the following formula to do so:
`m=(y_2-y_1)/(x_2-x_1)`, where
`(x_1,y_1)` and
`(x_2,y_2)` are points.

We can label the values of the points to help us.

`x_1=0\\y_1=5\\x_2=4\\y_2=1`

Now, substitute into the formula.

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

`m=(1-5)/(4-0)`

`m=(-4)/(4)`

m = -1

The slope of the line is -1.

Part C

We want to write the equation of the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Since we found the slope from part B, we can substitute that value in as m in the formula.

We now have:

y = -1x + b

This can be rewritten to:

y = -x + b

You may notice that the point (0,5) is on the y-axis, meaning that the line intersects the y-axis there, so it is the y-intercept.

The value of y at this point is 5.

So, b is equal to 5.

Substitute this value into the equation.

y = -x + 5