Question

Write the equation of any line parallel to Y=2(x+3)-4

Answer 1

Explanation:

`\text{The slope-intercept form of an equation of a line}:\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\\\\k:y=m_1x+b_1\\l:y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\=======================`

`\text{Parallel lines have the same slope}.\\\\\text{We have}\ y=2(x+3)-4=(2)(x)+(2)(3)-4=2x+6-4=2x+2\\\\\text{The slope}\ m=2.\\\\\text{All parallel lines to the given line have the equation:}\\\\y=2x+b\\\\\text{where}\ b\ \text{is any real number except 2}.`

Answer 2

y=2(x+3)

Explanation:

Here's the deal; a line parallel to another line has the same slope; it is just the y-intercept that is different. So, for this question, you can write the equation y=2(x+3) - b, where b ≠ 4.