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Sergeeva-Olga [200]
3 years ago
15

Through (-1,4) and a perpendicular to 4y-2x=12

Mathematics
1 answer:
mart [117]3 years ago
4 0

Answer:

<h2>y = -2x + 2 → 2x + y = 2</h2>

Step-by-step 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\\\\\text{then}\\\\k\ \perp\ l\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\k\ ||\ l\iff m_1=m_2

\text{We have the equation of a line in the standard form:}\ Ax+By=C.\\\\\text{Convert to the slope-intercept form:}\\\\4y-2x=12\qquad\text{add}\ 2x\ \text{to the both sides}\\\\4y-2x+2x=2x+12\\\\4y=2x+12\qquad\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{2x}{4}+\dfrac{12}{4}\\\\y=\dfrac{1}{2}x+3\to\boxed{m_1=\dfrac{1}{2}}

\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{Put the value of the slope and the coordinates of the given point (-1, 4)}\\\text{to the equation of a line:}\\\\4=-2(-1)+b\\\\4=2+b\qquad\text{subtract 2 from the both sides}\\\\4-2=2-2+b\\\\2=b\to b=2\\\\\bold{FINALLY:}\ y=-2x+2

\text{Convert to the standard form:}\\\\y=-2x+2\qquad\text{add}\ 2x\ \text{to the both sides}\\\\y+2x=-2x+2x+2\\\\2x+y=2

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