Question

Writing Equations of Parallel Lines

Answer 1

Answer:

The slope of the parallel line to the given line is $-\frac{1}{4}$

The equation of the parallel line to the given line and passes through the given point is y + 4 =  $-\frac{1}{4}$ (x + 2)

The y-intercept of the parallel line to the given line and passes through the given point is  $-\frac{9}{2}$

Step-by-step explanation:

• The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m = $\frac{y2-y1}{x2-x1}$

• 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 = $\frac{8-6}{-6-2}$ = $\frac{2}{-8}$ = $-\frac{1}{4}$

∴ The slope of the given line is $-\frac{1}{4}$  

∵ Parallel lines have the same slopes

∴ The slope of the parallel line to the given line is $-\frac{1}{4}$

∵ The parallel line passes through the point (-2, -4)

∴ x1 = -2 and y1 = -4

∵ m = $-\frac{1}{4}$

→ Substitute them in the point-slope form above

∵ y - (-4) = $-\frac{1}{4}$ (x - (-2))

∴ y + 4 =  $-\frac{1}{4}$ (x + 2)

∴ The equation of the parallel line to the given line and passes through

   the given point is y + 4 =  $-\frac{1}{4}$ (x + 2)

∵ m = $-\frac{1}{4}$

→ Substitute it in the slope-intercept form above

∴ y =  $-\frac{1}{4}$ x + b

→ To find b substitute x by -2 and y by -4 (coordinates the given point)

∵ -4 = $-\frac{1}{4}$(-2) + b

∴ -4 = $\frac{1}{2}$ + b

→ Subtract  $\frac{1}{2}$  from both sides

∴ $-\frac{9}{2}$ = b

∵ b is the y-intercept

∴ The y-intercept of the parallel line to the given line and passes

   through the given point is  $-\frac{9}{2}$