passing through (-2,1 ) and perpendicular to
4x + 7y + 3 = 0.

Step-by-step explanation:

The slope-intercept form of an equation of a line:

m - slope

b - y-intercept

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Let

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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:

            subtract 7y from both sides

        divide both sides by (-7)

Therefore

We have the equation:

Put the coordinates of the point (-2, 1) to the equation, and solve for b :

    multiply both sides by 2

          add 7 to both sides

           divide both sides by 2

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:

- slope-intercept form

Convert to the general form:

        multiply both sides by 4

     subtract 4y from both sides