Question

The line y = x + passes through (−3, 7) and is parallel to y = 4x − 1.

Answer 1

The line y = 4x + 19 passes through (−3, 7) and is parallel to y = 4x − 1.

Explanation:

Answer 2

parallel lines have exactly the same slope.

so this line will have the same slope as y = 4x - 1, so

`\bf y=\stackrel{\downarrow }{4}x-1\qquad \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}`

so, we're really then, looking for the equation of a line that has a slope of 4, and runs through -3, 7.

`\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies 4 \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=4[x-(-3)]\implies y-7=4(x+3) \\\\\\ y-7=4x+12\implies y=4x+19`