How do you write a slope-intercept equation for a line parallel to the line x-2y=6 which passes through the point (-5,2)?

Question

Eli Assouline · Accepted Answer

#y = 1/2 x + 9/2#

We know, If there are two equations of line like #a_1x + b_1y + c_1 = 0# and #a_2x + b_2x + c_2 = 0# ;

then, the condition of they being parallel is

#a_1/a_2 = b_1/b_2 != c_1/c_2#

First Convert the line equation to the general form #ax + by + c = 0#

Therefore, #x - 2y = 6#

#rArr x - 2y - 6 = 0# ..........................(i)

Then, the equation of parallel line will be

#x - 2y + k = 0# ........................................(ii) (k can be any constant)

If it passes through the point (-5, 2), then the equation will be satisfied with these values.

Lets put #x = -5# and #y = 2# in eq(ii).

Therefore, #x - 2y + k = 0# #rArr (-5) - 2(2) +k = 0# #rArr -5 - 4 + k = 0# #rArr k = 9#

Then the required equation will be #x - 2y + 9 = 0#.

The equation, at slope-intercept form is

#x - 2y + 9 = 0# #rArr -2y = -x - 9# #rArr 2y = x + 9# #rArr y = 1/2 x + 9/2#, where the slope is #m = 1/2# and the y-intercept is #c = 9/2#.

graph{y = (x + 9)/2 [-20.27, 20.26, -10.14, 10.13]}

Eva Abramson · Answer

#y=1/2x+9/2#

#• " parallel lines have equal slopes"#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

"Rearrange x-2y=6 into this form"

#rArry=1/2x-3larr" with "m=1/2#

#rArry=1/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-5,2)" into the partial equation"#

#2=-5/2+brArrb=9/2#

#rArry=1/2x+9/2larrcolor(red)"in slope-intercept form"#

Savannah Anderson · Answer

undefined To write a slope-intercept equation for a line parallel to the line $x - 2y = 6$ which passes through the point $(-5,2)$:

1. Rewrite the given equation in slope-intercept form: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
2. Determine the slope ($m$) of the given line.
3. The slope of a line parallel to the given line will be the same.
4. Use the point-slope form of a linear equation: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is the given point.
5. Substitute the slope ($m$) and the coordinates of the given point into the point-slope form.
6. Solve for $y$ to obtain the slope-intercept equation.

Let's solve:

1. Given equation: $x - 2y = 6$  
   Rewrite in slope-intercept form: $y = \frac{1}{2}x - 3$
2. Slope ($m$) of the given line is $\frac{1}{2}$.
3. Since the line we want is parallel, its slope is also $\frac{1}{2}$.
4. Using point-slope form with the given point $(-5,2)$:
   $y - 2 = \frac{1}{2}(x + 5)$
5. Simplify:
   $y - 2 = \frac{1}{2}x + \frac{5}{2}$
6. $y = \frac{1}{2}x + \frac{5}{2} + 2$  
   $y = \frac{1}{2}x + \frac{9}{2}$

So, the slope-intercept equation for the line parallel to $x - 2y = 6$ passing through $(-5,2)$ is $y = \frac{1}{2}x + \frac{9}{2}$.