Question

Write the equation of the line that is parallel to the line y=-7/4x-2 through the point (4,2)! Help please

Answer 1

as you already know, the equation y=-7/4x-2, is already in slope-intercept form and thus its slope is the coefficient of the "x", namely -7/4.

parallel lines have the same exact slope, so a parallel line to this one will also have a slope of -7/4, and it passes through 4,2,

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad \qquad \qquad slope = m\implies -\cfrac{7}{4} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-\cfrac{7}{4}(x-4) \\\\\\ y-2=-\cfrac{7}{4}x+7\implies y=-\cfrac{7}{4}x+9$