Find an equation of the line satisfying the conditions. Write the equation in slope-intercept form.
-Through $(-6,7)$; parallel to $3 x+7 y=3$
A) $y=\frac{3}{7} x+\frac{3}{7}$
B) $y=-\frac{7}{3} x+\frac{7}{3}$
C) $y=-\frac{3}{7} x+\frac{31}{7}$
D) $y=\frac{3}{7} x-\frac{31}{7}$

Question

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given line $3x + 7y = 3$ can be rewritten in slope-intercept form as $y = -\frac{3}{7}x + \frac{3}{7}$, indicating a slope of $-\frac{3}{7}$. To find the equation of a line parallel to the given line and passing through $(-6,7)$, we use the slope $-\frac{3}{7}$ and the point $(-6,7)$ in the point-slope form equation $y - y_1 = m(x - x_1)$, which simplifies to $y = -\frac{3}{7}x + \frac{31}{7}$ in slope-intercept form.

Find an Equation of the Line Satisfying the Conditions (−6,7)(-6,7)(−6,7) ; Parallel To

Find an Equation of the Line Satisfying the Conditions $(-6,7)$ ; Parallel To