Work out the equation of the line which passes through the point [tex](-1, 2)[/tex] and is parallel to the line [tex]y = x + 4[/tex].

Optional working:

Answer: _______________



Answer :

Sure, let's find the equation of the line that passes through the point [tex]\((-1, 2)\)[/tex] and is parallel to the line [tex]\(y = x + 4\)[/tex].

### Step-by-Step Solution:

1. Determine the Slope of the Given Line

The given line is [tex]\(y = x + 4\)[/tex]. This equation is in the slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope and [tex]\(b\)[/tex] is the y-intercept.

Here, [tex]\(m = 1\)[/tex] because the coefficient of [tex]\(x\)[/tex] is 1.

2. Recognize that Parallel Lines Have the Same Slope

Since the new line we are finding is parallel to [tex]\(y = x + 4\)[/tex], it will have the same slope. Therefore, the slope [tex]\(m\)[/tex] of our new line is also 1.

3. Use the Point-Slope Form of a Line Equation

The point-slope form of a line equation is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.

Substituting the given point [tex]\((-1, 2)\)[/tex] and the slope [tex]\(m = 1\)[/tex] into the point-slope form:
[tex]\[ y - 2 = 1(x - (-1)) \][/tex]
[tex]\[ y - 2 = 1(x + 1) \][/tex]

4. Simplify the Equation

Distribute the 1 on the right-hand side:
[tex]\[ y - 2 = x + 1 \][/tex]

Add 2 to both sides to solve for [tex]\(y\)[/tex]:
[tex]\[ y = x + 3 \][/tex]

Thus, the equation of the line that passes through the point [tex]\((-1, 2)\)[/tex] and is parallel to the line [tex]\(y = x + 4\)[/tex] is:

[tex]\[ \boxed{y = x + 3} \][/tex]