Y = mx + b, help

[mucpa2011]

" In the coordinate plane, line k passes through the origin and has a slope of 2. If points (3,y) and (x,4) are on line k, then x+y = ?"

Solution: "Since line k has slope 2 and passes through the origin, the equation of line k is y=2x. If the point (3,y) is on line k, then y = 2(3) = 6. If the point (x,4) is on line k, then 4 = 2x and so x=2. Therefore, x+y = 2+6 = 8."

I'm confused about the line that reads "...through the origin, the equation of line k is y=2x". Isn't that only part of the equation? Shouldn't it say "y=2x+b"?

 

[Mrspi]

" In the coordinate plane, line k passes through the origin and has a slope of 2. If points (3,y) and (x,4) are on line k, then x+y = ?"

Solution: "Since line k has slope 2 and passes through the origin, the equation of line k is y=2x. If the point (3,y) is on line k, then y = 2(3) = 6. If the point (x,4) is on line k, then 4 = 2x and so x=2. Therefore, x+y = 2+6 + 8."

I'm confused about the line that reads "...through the origin, the equation of line k is y=2x". Isn't that only part of the equation? Shouldn't it say "y=2x+b"?

In the equation y = mx + b,

b represents the y-intercept, or the point on the y-axis where the graph crosses that axis. The ORIGIN is the point (0, 0). If the graph crosses the y-axis at the origin, then the y-intercept is 0, and that will be the value of "b" in the equation

y = mx + b

"m" is the slope of the line.

Now, in your problem, you know that the slope is 2.

If we substitute 2 for m, and 0 for b, we have this equation:

y = 2*x + 0
y = 2x

I hope that helps.

 

[pka]

" In the coordinate plane, line k passes through the origin and has a slope of 2. If points (3,y) and (x,4) are on line k, then x+y = ?"

The equation is \(\displaystyle y=2x~.\)
So if both \(\displaystyle (3,~?)~\&~(?,4)\) are on that line find the values of the \(\displaystyle ?\).

 

[mmm4444bot]

Shouldn't it say "y=2x+b"?

No, because b = 0.

2x + 0 is the same as 2x.