Question

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Answer 1

The general form of the equation of a line is given by;

`y=mx+b`

where m is the slope of the line and b is the y-intercept.

You have the following equation of a line:

`y=2x-5`

a) By comparing the previous equation with the general form of the equation of a line, you can notice that the slope of the line is m = 2.

b) Any equation of a line with the same slope will be parallel to the line

y = 2x - 5.

c) You use the following formula for the slope of a line:

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

where (x1,y1) is a point of the line.

If you replace the given point (-2 , -1) in the previous equation, if you also replace the value of m and solve for y, you obtain:

`\begin{gathered} m=(y-(-1))/(x-(-2)) \\ m=(y+1)/(x+2) \\ m(x+2)=y+1 \\ m(x+2)-1=y \\ mx+2m-1=y \\ 2x+2(2)-1=y \\ 2x+4-1=y \\ 2x+3=y \end{gathered}`

Which is the same as:

y = 2x + 3

Hence, the equation y = 2x + 3 is a line parallel to the line y = 2x - 5 and passes trough the point (-2,-1)