What is an equation of the line that passes through the point (- 6, - 8) and is parallel to the line x - 2y = 6 ?

Answer 1

Fact being tested: Parallel lines have the same slope.

For a line written in slope-intercept form (y=mx+b), that slope is m.

If you convert a line from Standard Form (Ax+By=C), to slope-intercept form, that slope is (-A/B).

The question gives the equation x-2y=6. The parallel line has the equation, in Standard Form, or x-2y=C. Use the point to find C:

x-2y = C

(-6)-2(-8) = C

10 = C

In Standard Form, "an equation" for the parallel line is: x - 2y = 10

Answer 2

x - 2y = 6

Convert to slope-intercept form:

x - 6 = 2y y = x/2 - 3, so the slope of the original equation is 1/2.

For the eqn of a parallel line through (-6, -8), use same slope with the given point to find b, the y-intercept.

-8 = 1/2(-6) + b b = -8 + 3 = -5

The equation of a parallel line through (-6,-8) is y = x/2 - 5

Use the Desmos Graphing Calculator site to view the two parallel lines.

Answer 3

First thing we do in any math problem is write down our known information and rewrite the equation.

We know that slope-intercept form is y=mx+b and we have a point (-6,-8). We also know that two lines are parallel if they have the same slope and we are given the equation x-2y=6.

We will rewrite the given equation in slope intercept form: y=.5x-3. This means that our original line has a slope of 0.5 and a y intercept of -3.

Since we know that our new line will have the same slope, we can go ahead and write out y=0.5x+b and we will need to solve for b using out point. If we plug in x=-6 and y=-8, we can solve for the y intercept of our parallel line.

-8=0.5(-6)+b

-8=-3+b

-5=b

y=0.5x-5

Answer 4

Answer 5