Question

I'm attempting to solve and linear equation out of ordered pairs in slopes attached

Answer 1

Line equation

Initial explanation

We know that the equation of a line is given by

y = mx + b,

where m and b are numbers: m is its slope (shows its inclination) and b is its y-intercept.

In order to find the equation we must find m and b.

In all cases, m is given, so we must find b.

We use the equation to find b:

y = mx + b,

↓ taking mx to the left side

y - mx = b

We use this equation to find b.

1

We have that the line passes through

(x, y) = (-10, 8)

and m = -1/2

Using this information we replace in the equation we found:

y - mx = b

↓ replacing x = -10, y = 8 and m = -1/2

`\begin{gathered} 8-(-(1)/(2))\mleft(-10\mright)=b \\ \downarrow(-(1)/(2))(-10)=5 \\ 8-5=b \\ 3=b \end{gathered}`

Then, the equation of this line is:

y = mx + b,

↓

y = -1/2x + 3

Equation 1: y = -1/2x + 3

2

Similarly as before, we have that the line passes through

(x, y) = (-1, -10)

and m = 0

we replace in the equation for b,

y - mx = b

↓ replacing x = -1, y = -10 and m = 0

-10 - 0 · (-1) = b

↓ 0 · (-1) = 0

-10 - 0 = b

-10 = b

Then, the equation of this line is:

y = mx + b,

↓

y = 0x - 10

y = -10

Equation 2: y = -10

3

Similarly as before, we have that the line passes through

(x, y) = (-6, -9)

and m = 7/6

we replace in the equation for b,

y - mx = b

↓ replacing x = -6, y = -9 and m = 7/6

`\begin{gathered} -9-(7)/(6)(-6)=b \\ \downarrow(7)/(6)(-6)=-7 \\ -9-(-7)=b \\ -9+7=b \\ -2=b \end{gathered}`

Then, the equation of this line is:

y = mx + b,

↓

y = 7/6x - 2

Equation 3: y = 7/6x - 2

4

The line passes through

(x, y) = (6, -4)

and m = does not exist

When m does not exist it means that the line is vertical, and the equation looks like:

x = c

In this case

(x, y) = (6, -4)

then x = 6

Then

Equation 4: x = 6

5

The line passes through

(x, y) = (6, -6)

and m = 1/6

we replace in the equation for b,

y - mx = b

↓ replacing x = 6, y = -6 and m = 1/6

`\begin{gathered} -6-(1)/(6)(6)=b \\ \downarrow(1)/(6)(6)=1 \\ -6-(1)=b \\ -7=b \end{gathered}`

Then, the equation of this line is:

y = mx + b,

↓

y = 1/6x - 7

Equation 5: y = 1/6x - 7