Answer:
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
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Let
[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2[/tex]
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We have the equation of a line in a general form (Ax + By + C = 0)
Convert it to the slope-intercept form:
[tex]4x+7y+3=0[/tex] subtract 7y from both sides
[tex]4x+3=-7y[/tex] divide both sides by (-7)
[tex]-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}[/tex]
Therefore
[tex]m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}[/tex]
We have the equation:
[tex]y=\dfrac{7}{4}x+b[/tex]
Put the coordinates of the point (-2, 1) to the equation, and solve for b :
[tex]1=\dfrac{7}{4}(-2)+b[/tex]
[tex]1=-\dfrac{7}{2}+b[/tex] multiply both sides by 2
[tex]2=-7+2b[/tex] add 7 to both sides
[tex]9=2b[/tex] divide both sides by 2
[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]
Finally:
[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] - slope-intercept form
Convert to the general form:
[tex]y=\dfrac{7}{4}x+\dfrac{9}{2}[/tex] multiply both sides by 4
[tex]4y=7x+18[/tex] subtract 4y from both sides
[tex]0=7x-4y+18[/tex]
