Question

hat is the slope-intercept form of the function described by this table? x 1 2 3 4 y −2 −6 −10 −14 Enter your answers in the boxes. y = x +

Answer 1

Slope intercept form:- An equation of line is in the form of y =mx +b .....[1] ; where m is the slope and b is the y-intercept.

Consider any two point from the table i.e,

(1, -2) and (2 , -6)

Calculate first slope of these points:

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

then;

`m=(-6+2)/(2-1)=(-4)/(1)=-4`

then; substitute the value of m in [1]

Equation of line is;

`y=-4x+b` ......[2]

Now, substitute any coordinate point from the table i.e (3 , -10) in [2] to solve for b;

-10 = -4(3) +b

-10 = -12 +b

Add both sides 12 we get;

-10 + 12 = -12 +b +12

Simplify:

2 = b

Equation of line is; y = -4x+2

Therefore, the slope intercept form of the function describe by the given table is;

y = -4x +2