Explanation:
To find the equation of a line parallel to the given equation y = 3x + 2 that passes through the points (-1, 3) and (-3, 1), you can use the fact that parallel lines have the same slope.
1. Start with the slope of the original line, which is 3 (the coefficient of x).
2. Now, use the point-slope form of a linear equation to find the equation of the parallel line. The point-slope form is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line, and m is the slope.
3. Pick one of the given points. Let's use (-1, 3):
y - 3 = 3(x - (-1))
4. Simplify:
y - 3 = 3(x + 1)
5. Now, you can convert this equation into the slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept:
y - 3 = 3x + 3
6. Add 3 to both sides:
y = 3x + 3 + 3
7. Simplify further:
y = 3x + 6
So, the equation of the line parallel to y = 3x + 2 that passes through the points (-1, 3) and (-3, 1) is:
y = 3x + 6