Question

Write the equation of a line parallel to the line 2x + y = 3 that passes through the point (2,6)

Answer 1

Answer (assuming it can be in slope-intercept form):

$y = -2x +10$    

Step-by-step explanation:

1) First, we need to find the slope of the given equation. To do that easily, convert it to slope-intercept form, represented by the formula  $y = mx + b$. Isolate y:

$2x + y = 3\\y = -2x + 3$

The number in place of $m$, or the coefficient of the x-term, represents the slope of the equation. So, the slope of the given equation is -2.

Lines that are parallel share the same slope. So, the slope of the new equation will be -2 as well.  

2) Now, remember that the slope-intercept form is represented by the formula $y = mx + b$. In order to write an equation of a line using that formula, we need to substitute values for $m$ and $b$. We know $m$ is the slope, so we already know what that equals. Now, we just need to find $b$.

To do that, substitute -2 for $m$ in the slope-intercept formula. Additionally, substitute the x and y values of the point (2,6) for the x and y in the formula as well. This sets up the equation so that we can isolate $b$ and find its values:  

$y = mx +b\\6 = (-2)(2)+b\\6 = -4 + b\\10 = b$

So, $b$ = 10.

3) Substitute values for $b$ and $m$ into the slope-intercept formula to write the slope-intercept form of the line:

$y = -2x +10$