Question

an equation in slope-intercept form for the line that passes through (4,-4) and is parallel to 3+4x=2y-9

Answer 1

`\large\boxed{y=-(1)/(2)x-2}`

Explanation:

`\text{The slope-intercept form:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\======================`

`\text{If}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2\ \text{are\ parallel, then}\ m_2=-(1)/(m_1)\\===========================`

`\text{We have the equation of a line:}\ 3+4x=2y-9.\\\text{Convert it to the slope-intercept form:}\\\\2y-9=3+4x\qquad\text{add 9 to both sides}\\\\2y=12+4x\qquad\text{divide both sides by 2}\\\\y=6+2x\\\\y=2x+6\to m_1=2\\\\\text{therefore}\ m_2=-(1)/(2)\\\\\text{We have the equation:}\ y=-(1)/(2)x+b\\\\\text{Put the coordinates of the given point (4, -4) to the equation:}\\\\-4=-(1)/(2)(4)+b\\\\-4=-2+b\qquad\text{add 2 to both sides}\\\\-2=b\to b=-2\\\\\text{Finally we have the equation:}\ y=-(1)/(2)x-2`