Question

How do you write the equation of the line parallel to y = 3x - 4 and passing through the point (-2, 5)?

Answer 1

`y =3x+11`

Explanation:

Parallel lines have the same slopes.

The slope of the new line will have the same slope as the given line:

`y = color(red)(3)x -4 rArr m= color(red)(3)`

One point on the line is given, `color(blue)(((-2, 5))). "This is " color(blue)(((x_1, y_1)))`

The formula for slope is `m = ("change in y values"/"change in x-values") = (y_2-y_1)/(x_2-x_1)`

If you have the slope and one point , substitute them into a formula which is based on the formula for slope given above.

`y-color(blue)(y_1) = color(red)(m)(x-color(blue)(x_1))`

`y-color(blue)(5) = color(red)(3)(x-color(blue)((-2)))`
`y-5 =3(x+2)`

Simplify to get the required equation of the line.

`y = 3x+6+5`

`y =3x+11`