Part 6 Passes through (-6, 10) & (-3, -2)
Slope:
Y-Intercept:
Equation of the line:


Hey there! I'm happy to help!

SLOPE

To find the slope, you divide the difference of the y values by the difference in the x values.

10-(-2)=10+2=12

-6-(-3)=-6+3=-3

12/-3=-4

So, our slope is -4.

Y- INTERCEPT

To find the y-intercept, we plug our slope and one of our points into the slope intercept equation (y=mx+b) and solve for b, which is the y-intercept. We will use the point (-6,10).

10=-4(-6)+b

Flip the equation so b is on the left.

-4(-6)+b=10

24+b=10

Subtract 24 from both sides.

b=-14

Our y-intercept is -14.

EQUATION

The slope intercept equation is y=mx+b, where m is the slope and b is the y-intercept. Therefore, we have the following answers.

Slope: -4

y-Intercept: -14

Equation of the Line: y=-4x-14

Have a wonderful day! :D

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1