Question

What is the equation of a line that is parallel to the line with the equation y=2/3x+2 and passes threw the point 1,-1

Answer 1

The equation of line parallel to given line is: $y = \frac{2}{3}x-\frac{5}{3}$

Step-by-step explanation:

Given equation of line is:

$y = \frac{2}{3}x+2$

As the line is in slope-intercept form, the co-efficient of x is the slope of the line

So,

$m_1 =\frac{2}{3}$

Let m2 be the slope of required line

As both the lines are parallel,

$m_1 = m_2$

So,

$m_2 = \frac{2}{3}$

The slope intercept form of line is:

$y = mx+b$

Putting the value of the slope

$y = \frac{2}{3}x+b$

To find the value of b, putting (1,-1) in the equation

$-1 = \frac{2}{3}(1) +b\\-1 = \frac{2}{3} +b\\b = -1-\frac{2}{3}\\b = \frac{-3-2}{3}\\b = \frac{-5}{3}$

Putting b=-5/3 in the equation

$y = \frac{2}{3}x-\frac{5}{3}$

Hence,

The equation of line parallel to given line is: $y = \frac{2}{3}x-\frac{5}{3}$

Keywords: Equation of line, slope

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