Respuesta :
Answer:
The slope of the parallel line to the given line is [tex]-\frac{1}{4}[/tex]
The equation of the parallel line to the given line and passes through the given point is y + 4 = [tex]-\frac{1}{4}[/tex] (x + 2)
The y-intercept of the parallel line to the given line and passes through the given point is [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
- The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]
- The point-slope form of the linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line
- The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept
- Parallel lines have the same slopes and different y-intercepts
In the given figure
∵ The given line passes through points (2, 6) and (-6, 8)
∴ x1 = 2 and y1 = 6
∴ x2 = -6 and y2 = 8
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{8-6}{-6-2}[/tex] = [tex]\frac{2}{-8}[/tex] = [tex]-\frac{1}{4}[/tex]
∴ The slope of the given line is [tex]-\frac{1}{4}[/tex]
∵ Parallel lines have the same slopes
∴ The slope of the parallel line to the given line is [tex]-\frac{1}{4}[/tex]
∵ The parallel line passes through the point (-2, -4)
∴ x1 = -2 and y1 = -4
∵ m = [tex]-\frac{1}{4}[/tex]
→ Substitute them in the point-slope form above
∵ y - (-4) = [tex]-\frac{1}{4}[/tex] (x - (-2))
∴ y + 4 = [tex]-\frac{1}{4}[/tex] (x + 2)
∴ The equation of the parallel line to the given line and passes through
the given point is y + 4 = [tex]-\frac{1}{4}[/tex] (x + 2)
∵ m = [tex]-\frac{1}{4}[/tex]
→ Substitute it in the slope-intercept form above
∴ y = [tex]-\frac{1}{4}[/tex] x + b
→ To find b substitute x by -2 and y by -4 (coordinates the given point)
∵ -4 = [tex]-\frac{1}{4}[/tex](-2) + b
∴ -4 = [tex]\frac{1}{2}[/tex] + b
→ Subtract [tex]\frac{1}{2}[/tex] from both sides
∴ [tex]-\frac{9}{2}[/tex] = b
∵ b is the y-intercept
∴ The y-intercept of the parallel line to the given line and passes
through the given point is [tex]-\frac{9}{2}[/tex]