what is an equation of the line that passes through the point (6,3) and is parallel to the line x+3y=24

Answer 1

Initially, to get the slope of the original line, we need to correctly write this in slope-intercept form. This requires solving this equation for y:

x + 3y = 24

3y = -x + 24

y = -(1/3)x + 8 --> The slope of this line is -1/3. Parallel lines have equal slopes, therefore the slope of the new line will also be -1/3

We can continue this process by starting with the point-slope formula and convert to the slope-intercept form:

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

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

y = (-1x/3) + 5

The equation of the new line is y = (-1/3)x + 5