Find the equation of a line that contains the points (4,−1) and (−1,−4). Write the equation in slope-intercept form, using fractions when required.

y = 3/5x - 17/5

Step-by-step explanation:

slope formula: (y₂ - y₁) / (x₂ - x₁)

First, plug in these values of the two given points.

(-4 - (-1)) / (-1 - 4)

Simplify within the parentheses.

(-4 + 1) / (-1 - 4)

(-3) / (-5)

3/5

This is your slope. Plug this into a standard slope-intercept equation: y = mx + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (-1, -4). Plug in the x and y values into the x and y of the standard equation.

-4 = 3/5(-1) + b

Multiply.

-4 = -3/5 + b

Add 3/5 to both sides. -- To add it easier, convert 4 to a have a denominator of 5.

-20/5 = -3/5 + b

-20/5 + 3/5 = b

-17/5 = b

Now, plug this into your standard equation.

y = 3/5x - 17/5

Check this equation by plugging in the other point you did not use (4, -1)

-1 = 3/5(4) - 17/5

-1 = 12/5 - 17/5

-1 = -5/5

-1 = -1

Your answer is correct!

Hope this helps!

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!

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.