Use the given conditions to write an equation for the line in the indicated form. Passing through \( (4,3) \) and perpendicular to the line whose equation is \( y= \) \( 8 x+7 \); point-slope form

To find the equation of a line that passes through the point \( (4,3) \) and is perpendicular to the given line \( y = 8x + 7 \), we first need to determine the slope of the given line, which is \( 8 \). The slope of a line that is perpendicular to another is the negative reciprocal of the original line's slope. Therefore, the slope of the new line will be \( -\frac{1}{8} \). Now we can use the point-slope form of a line, which is expressed as \( y - y_1 = m(x - x_1) \). Substituting in the point \( (4, 3) \) and the slope \( -\frac{1}{8} \), we get: \[ y - 3 = -\frac{1}{8}(x - 4) \]