Question

Find the equation of the line defined by Y1 that yields table of points. Give the equation in slope intercept formX -10 -9 -8 -7 -6 -5 -4Y1 -23 -19 -15 -11 -7 -3 1

Answer 1

From the given table, we have the points:

(x, y1) ==> (-10, -23), (-9, -19), (-8, -15), (-7, -11), (-6, -11), (-6, -7), (-5, -3), (-4, 1)

Let's write an equation in slope-intercept form using the given points.

Apply the slope-intercept form of a linear equation:

y = mx + b

Where m is the slope and b is the y-intercept.

To find the slope, m, apply the formula:

`m=(y2-y1)/(x2-x1)`

• Take any two points:

(x1, y1) ==> (-10, -23)

(x2, y2) ==> (-7, -11)

• Input the coordinates of the points in the formula for m:

`\begin{gathered} m=(-11-(-23))/(-7-(-10)) \\ \\ m=(-11+23)/(-7+10) \\ \\ m=(12)/(3) \\ \\ m=4 \end{gathered}`

The slope of the line, m, is 4.

Now, we have:

y = 4x + b

Plug in the coordinates of any point for x and y to solve for the y-intercept, b.

Take the last point:

(x, y) ==> (-4, 1)

We have:

1 = 4(-4) + b

1 = -16 + b

Add 16 to both sides:

1 + 16 = -16 + 16 + b

17 = b

b = 17

The y-intercept, b, is 17.

Therefore, the equation of the line in slope-intercept form is:

y = 4x + 17

ANSWER:

`y=4x+17`