Question

I need help on trying to find the slope and the y-intercept

Answer 1

Slope = -1

y-intercept = -3

Step-by-step explanation

We are asked to find the slope and the y-intercept of the function whose data points are presented

To find slope of a function, the slope of the function can be obtained when the coordinates of two points of the function are known. If the points are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

So, for this function, we take the two most extreme points, so,

(x₁, y₁) and (x₂, y₂) are (-1, -2) and (5, -8)

x₁ = -1

y₁ = -2

x₂ = 5

y₂ = -8

`\text{Slope = }(-8-(-2))/(5-(-1))=(-8+2)/(5+1)=-(6)/(6)=-1`

Now that we have the slope of the line, we can then write the equation of the line and obtain the y-intercept eventually

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

Using the first point on the table,

x₁ = -1

y₁ = -2

m = -1

y - y₁ = m (x - x₁)

y - (-2) = -1 (x - (-1))

y + 2 = -1 (x + 1)

y + 2 = -x - 1

y = -x - 1 - 2

y = -x - 3

So, to obtain the y-intercept; the y-intercept is the value of y when x = 0

y = -x - 3

when x = 0

y = -x - 3

y = 0 - 3

y = -3

Hope this Helps!!!