What is the equation in slop-intercept form of the line that passes through the point (5,0) and is parallel to the line represented by 6x+3y=12 a: y=-2/3+7
b: y=6x-1
c: y=2x-2
d: y=-2x+10

d: y=-2x+10

Explanation:
There are a few concepts we need to understand when solving this problem. The first is what this form of a linear equation actually means: y=mx+b
Y=the y-coordinate
M=the slope
X=the x-coordinate
B=the y intercept (the point on h ty e line that crosses the y-axis)
This linear equation is called slope-intercept form.

The second thing we need to understand is that the equation 6x+3y=12 is organized into a different form of a linear equation: Ax+By=C. This is called the standard form of a linear equation.
A, B and C don’t mean anything that we can directly identify from a graph, which is why it’s best we reorganize this into slope-intercept form, where we can identify the slope and y intercept.

The last thing that we need to understand is that parallel lines have the same slopes.
Example: y=5x and y=5x+6 are parallel.

Knowing this, the first thing we should to is rearrange 6x+3y=12 into slope intercept form, and we do this by isolating y.

6x+3y=12
Subtract both sides by 6x
6x-6x+3y=-6x+12
3y=-6x+12
Divide both sides by 3
3y/3=(-6x+12)/3
y=-2x+4

From this equation, it is clear that -2 is in the position of m in y=mx+b, meaning that -2 is the slope of the given line.
Now, we can automatically rule out answer choices a, b and c since none of their slopes are -2, since parallel lines have the same slope.

I hope this helps!