Question

Passes through (-4, 2 ) and parallel to y = 1/2x + 5

Answer 1

`\large\boxed{y=(1)/(2)x+4}`

Explanation:

`\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-(1)/(m_1)\\\\===========================\\\\\text{We have}\ k:y=(1)/(2)x+5\to m_1=(1)/(2)\\\\\text{Let}\ l:y=m_2x+b.\\\\l\ \parallel\ k\iff m_2=m_1\to m_2=(1)/(2).\\\\l:y=(1)/(2)x+b\\\\\text{Put the coordinates of the given point (-4, 2) to the equation of a line:}\\\\2=(1)/(2)(-4)+b\\\\2=-2+b\qquad\text{add 2 to both sides}\\\\4=b\to b=4\\\\\text{Finally:}\\\\y=(1)/(2)x+4`

Answer 2

y = 1/2x + 4

Explanation:

Lines that are parallel have the same gradient....in which its 1/2

Equation of the line that is parallel to y = 1/2x + 5 and passes through (-4,2)

(y - 2) = 1/2(x + 4)

2(y - 2) = x + 4

; 2y - 4 = x + 4

Equation of the line,

y = 1/2x + 4