Question

Write a linear equation of a line that passes through (7,4) and (5,0)

Answer 1

`y=2x-10`

Step-by-step explanation

Step 1

find the slope of the line

when you know 2 points of a line ( P1 and P2) , you can find the slope by using:

`\begin{gathered} \text{slope}=\frac{change\text{ in y }}{\text{change in x}}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_(_2),y_2) \end{gathered}`

then, Let

P1(7,4)

P2(5,0)

replace,

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(0-4)/(5-7) \\ \text{slope}=(-4)/(-2) \\ \text{slope}=2 \end{gathered}`

Step 2

now, find the equation of the line

`\begin{gathered} y-y_1=sl_{}ope(x-x_1) \\ \text{where} \\ P1(x_1,y_1)\text{ is a known point of the line} \end{gathered}`

Let

P1(7,4)

now, replace

`\begin{gathered} y-y_1=sl_{}ope(x-x_1) \\ y-4=2(x-7) \\ y-4=2x-14 \\ \text{add 4 in both sides} \\ y-4+4=2x-14+4 \\ y=2x-10 \end{gathered}`

so, the answer is

`y=2x-10`

I hope this helps you