What is an equation of the line that passes through the point (3,6)(3,6) and is parallel to the line 4x-3y=214x−3y=21?

Question:

What is an equation of the line that passes through the point (3,6) and is parallel to the line 4x-3y=21

The equation of the line that passes through the point (3,6) and is parallel to the line 4x-3y=21 is:

Solution:

Given that line passes through the point (3,6) and is parallel to the line 4x-3y=21

The equation of line in slope intercept form is given as:

y = mx + c ------- eqn 1

Where, "m" is the slope and "c" is the y intercept

Given equation is:

4x - 3y = 21

Rearrange,

3y = 4x - 21

On comparing above equation with eqn 1,

We know that slopes of parallel lines are same

Therefore, slope of line parallel to the line 4x - 3y = 21 is 4/3

Substitute m = 4/3 and (x, y) = (3, 6) in eqn 1

Substitute c = 2 and m = 4/3 in eqn 1

Thus the equation of line is found

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.