Respuesta :
Answer
Slope = -1
y-intercept = -3
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
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]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
[tex]\text{Slope = }\frac{-8-(-2)}{5-(-1)}=\frac{-8+2}{5+1}=-\frac{6}{6}=-1[/tex]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!!!
