What is "3x=9" in y=mx+b form, and what is its slope, y-intercept, and x-intercept? [i think that its x-intercept is (3,0), but i'm not sure about any of the others]
Also, what is the x-intercept of "2y+16=0"? [is it "none"?]
I think these are trick questions and you have the right idea.
3x = 9 is the equation of a vertical line. There is no y in the equation, so there is no "y = mx + b" form for a vertical line. The simplest way to express this line is x = 3.
Its x-intercept is 3 (because (3, 0) is where the line crosses the x-axis).
It does not have a y-intercept, because the line never crosses the y-axis.
Technically, it has an undefined slope.
Similarly, the other equation is a horizontal line. 2y + 16 = 0 is the same as 2y = -16, or y = -8. This is a horizontal line through (0, -8). It has no x-intercept. The y-intercept is -8. The slope is zero. I think you are right to say that the x-intercept is "none."
Thanks!!! No wonder why these questions didn't make much sense and didn't seem quite possible to solve...
However, if the equation was this instead ...
2y + 16x = 0
... then you do have a diagonal line that has both an x-intercept and a y-intercept and a slope that is not zero but not undefined. I think it is a negative slope.
Can you figure out the x-intercept of the line? the y-intercept of the line? and the slope of the line? Hint: When y = 0, what is x? That gives you one intercept. When x = 0, what is y? That gives you another intercept. Draw the line and see if you can find the slope.
To rewrite the equation "3x=9" in y=mx+b form, where m represents the slope and b represents the y-intercept, you need to solve the equation for y.
To do this, divide both sides of the equation by 3:
3x/3 = 9/3
x = 3
Thus, the equation "3x=9" in y=mx+b form will be y=0x+3, where the y-intercept is 3.
In this case, we can see that the coefficient of x is 0, which means there is no slope. Therefore, the slope is 0.
To find the x-intercept, we set y equal to zero in the equation and solve for x:
0=0x+3
0 - 3 = 0x
-3 = 0x
No matter what value you choose for x, the equation equals -3. Therefore, the x-intercept does not exist for this equation.
Now, let's consider "2y+16=0." To find the x-intercept, we need to solve the equation for x. However, in this case, we have an equation in terms of y, not x.
To find the x-intercept, we set y equal to zero in the equation and solve for x:
2(0) + 16 = 0
16 = 0
Since the equation 16=0 is not true for any value of x, there is no x-intercept for the equation "2y+16=0."