Question

I need help on all these questionsFind the equation of the lineHelp with number 10

Answer 1

y = (8/7)x + 33/7

Step-by-step explanation:

First, we need to calculate the slope of the line. So, we can use the following equation:

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

Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.

We can replace (x1, y1) with (-5, -1) and (x2, y2) with (2, 7) and get that the slope is equal to:

`m=(7-(-1))/(2-(-5))=(7+1)/(2+5)=(8)/(7)`

Now, the equation of a line with slope m that passes through the point (x1, y1) is:

`y-y_1=m(x-x_1)`

So, replacing m by 8/7 and (x1, y1) by (-5, -1), we get that the equation is:

`\begin{gathered} y-(-1)=(8)/(7)(x-(-5)) \\ y+1=(8)/(7)(x+5) \end{gathered}`

Finally, we can solve the equation for y and get:

`\begin{gathered} y+1=(8)/(7)x+(8)/(7)(5) \\ y+1=(8)/(7)x+(40)/(7) \\ y+1-1=(8)/(7)x+(40)/(7)-1 \\ y=(8)/(7)x+(33)/(7) \end{gathered}`

Therefore, the answer is:

y = (8/7)x + 33/7