Question

the line L4 passes through the point (0,3) and is parallel to the line y-x+3=0 .find the equation of L4

Answer 1

Answer:

$y\text{ = x + 3}$

Explanation:

Here, we want to get the equation of the line

The general equation of a straight line can be expressed as:

$y\text{ = mx + b}$

where m is the slope and b is the y-intercept (the point at which x = 0)

Now, let us write the given equation in the general form

We have this as:

$y\text{ = x-3}$

From here, we can see that the value of the slope which is the coefficient of x is 1

When two lines are parallel, the value of their slopes are equal

This mean that the value of the slope of the line L4 is 1 too

Finally, by using the point slope format, we can get the equation of the line L4

We have the point-slope form as:

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{where (x}_1,y_1)\text{ = (0,3)} \\ y-3\text{ = 1(x-0)} \\ y-3\text{ = x} \\ y\text{ = x + 3} \end{gathered}$