Question

Which equation best represents a trend line for the scatter plot?

y=−37x+4

y=73x+4

y=−73x+4

y=37x+4

Answer 1

Option A ic orrect.

`y=-(3)/(7)x+ 4`

Explanation:

Point slope form:

The equation of line is given by:

`y-y_1=m(x-x_1)` .....[1]

where m is the slope of line and a point
`(x_1,y_1)` lies on the line in the coordinate plane.

As per the statement:

You can see from the graph of line

We have two points i.e,

(0, 4) and (7, 1)

First calculate the slope:

`\text{Slope} = (y_2-y_1)/(x_2-x_1)`

then;

`\text{Slope}(m) = (1-4)/(7-0) = -(3)/(7)`

Now, substitute the value of m and (0,4) in [1] we have;

`y-4=-(3)/(7)(x-0)`

Simplify:

`y-4=-(3)/(7)x`

Add 4 to both sides we get;

`y=-(3)/(7)x+ 4`

Therefore, the equation best represents the trend line for the scatter plot is
`y=-(3)/(7)x+ 4`

Answer 2

y = (-3/7)x + 4

Looking at the graph, you can see the trend line plotted. And conveniently, there are a couple of points on the trend line that are indicated. Those points being (0,4) and (7,1). The equation of a line in slope intercept form is:y = ax+b

Looking at the points available, the point (0,4) already gives us the y intercept since x is equal to 0. So our equation becomes:
y = ax + 4

Now we need to determine a which is the slope. The slope is the change in y divided by the change in x. So let's do that
(1-4)/(7-0) = -3/7

And now our equation becomes:
y = (-3/7)x + 4

And given formatting issues, the first option available is the correct one.