Question

Write an equation of the line that passes through the given point and is parallel to the given line.

1. (1, 3); y = 2x - 5 2. (-2, 1); y = -4x + 3

Answer 1

1. Equation of line is y=2x+1

2. Equation of line is y=-4x-7

Explanation:

Theory :

Equation of line is given as y = mx + c.

Where, m is slope and c is y intercepted.

1.

Slope of given line : y = 2x-5 is m=2.

We know that line : y = 2x-5 is parallel to equation of target line.

therefore, slope of target line will be 2.

we write equation of target line as y=2x+c

Now, It is given that target line passes through point ( 1,3 ).

hence, point ( 1,3 ) satisfy the target line's equation.

we get,

y=2x+c

3=2
`*` 1 + c

3=2+c

c=1

thus, Equation of line is y=2x+1

2.

Slope of given line : y = -4x+3 is m= -4

We know that line : y = -4x+3 is parallel to equation of target line.

therefore, slope of target line will be -4

we write equation of target line as y=-4x+c

Now, It is given that target line passes through point ( -2,1 ).

hence, point ( -2,1 ) satisfy the target line's equation.

we get,

y=-4x+c

1= -4
`*` -2+ c

1=8+c

c=-7

thus, Equation of line is y=-4x-7