Question

What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

y = x + 4
y = x +
y = –5x + 4
y = –5x +

Answer 1

b

Explanation:

The given blue line passes through points (0, -3) and (-5, -4). This means that its slope m is

.

Any line parallel to this line has the same slope, that is 1/5.

Answer 2

The given blue line passes through points (0, -3) and (-5, -4). This means that its slope m is


`\displaystyle{ m= (y_2-y_1)/(x_2-x_1)=(-3-(-4))/(0-(-5))= (-3+4)/(5)= (1)/(5)`.

Any line parallel to this line has the same slope, that is 1/5.


The equation of the line with slope 1/5, passing through the point (-2, 2) is:


`y-2= (1)/(5)(x-(-2))\\\\y-2= (1)/(5)x+ (2)/(5)`.


Adding 2 to both sides, we have:


`y= (1)/(5)x +(12)/(5)`.


Answer:
`y= (1)/(5)x +(12)/(5)`.