Write an equation ​(a) in​ slope-intercept form and ​(b) in standard form for the line passing through ​(−3,6) and parallel to x+2y=5.

Question

I need help finding them in slope - intercept form and standard form. I am lost and I do not understand how to do this problem. 

Answer 1

The equation given can be re-written in slope-intercept form as y = (-1/2)x + (5/2)

 

The slope of the given line is -1/2 and the slope of any line parallel to this one will have equal slope.

 

The equation you need then is -1/2 = (y - 6)/(x + 3)

Remember slope is the change is y value (sometimes called rise) divided by the change in x value  (sometimes called run).

 

Cross multiplication and collection of terms will give you the standard form: x + 2y -9 = 0

and rearrangement will give you slope-intercept from: y = (-1/2)x + (9/2).

Answer 2

y=-x/2 + 9/2

is the equation through (-3,6) parallel to x+2y = 5

slope = coefficient of x term when the equation is solved for y = -x/2 +5/2

in point slope form the line's equation is

y -6 = (-1/2)(x+3)

in slope intercept form

y = -x/2 +9/2