Question

What is the equation of the line (in point-slope form) that passes through the point (2,3) and is parallel to the line y−9=2/3(x+7)?

Answer 1

The answer is y = -3/2x + 6

Explanation:

Answer 2

`\large\boxed{y-3=(2)/(3)(x-2)}`

Explanation:

`\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================`

`\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-slope\\\\(x_1,\ y_1)-point\ on\ a\ line\\\\===============================`

`\text{We have the equation of a line:}\ y-9=(2)/(3)(x+7)\to m_1=(2)/(3).\\\\\text{A slope of parallel line:}\ m_2=m_1=(2)/(3).\\\\\text{Put the value of the slope and the coordinates of the point (2, 3)}\\\text{to the equation of a line in point-slope form:}\\\\y-3=(2)/(3)(x-2)`