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Find the standard form of the equation of the line through (4, 1) that is perpendicular to the line 2x = -3y + 7. What is the x- and y-intercept of the line

moocake
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    What have you tried? – morrowmh Jul 30 '22 at 22:41
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    You can find out an equation of a line with a point and slope. So how can you find out the slope of the line you want? You can find the $x$ and $y$ intercepts from the equation. – fleablood Jul 30 '22 at 23:29
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    If line A has slope $~M \neq 0, ~$ and line B is perpendicular to line A, what have you been taught about the slope of line B, in terms of $~(M) ~$ ? – user2661923 Jul 30 '22 at 23:55

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Find the slope, m from the equation below: $$2x=-3y+7$$ $$2x-7=-3y$$ $$-3y=2x-7$$ $$y=-\frac{2}{3}x+\frac{7}{3}$$ $$m=-\frac{2}{3}$$

To find the perpendicular slope, let: $$m_1=-\frac{2}{3}$$

Use the formula: $$m_1m_2=-1$$ $$\left(-\frac{2}{3}\right)m_2=-1$$ $$m_2=\frac{3}{2}$$

Use the basic formula: $$y=mx+c$$ $$y=\frac{3}{2}x+c$$

Substitute the coordinate $(4,1)$ to get $c$ value: $$y=\frac{3}{2}x+c$$ $$1=\frac{3}{2}\left(4\right)+c$$ $$1=6+c$$ $$c=-5$$

Therefore: $$y=\frac{3}{2}x+c$$ $$y=\frac{3}{2}x-5$$

Reference picture: enter image description here

KMN
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