determine the slope, x-intercept, and y-intercept of the following equations
x - y = 0
y = 3x - 5
determine the slope, x-intercept, and y-intercept of the following equations
x - y = 0
y = 3x - 5
The best way to see the slope is to put each equation in the slope/y-intercept form. To do this, solve for y. One of these equations is already in the slope y-intercept form but the other is not. The slope/y-intercept form looks like this:
y=mx+b
M is the slope and b is the y-intercept.
For y=3x-5,
The slope is the coefficient of x, 3. The y-intercept is the value of y when x is 0. In this equation, it is -5. That is because when you plug in 0 for x, you get y=0x-5, or just y=-5.
The x-intercept is the value of x when y is 0. Plug in 0 for y:
0=3x-5
5=3x
5/3=x, the x-intercept.
Now let's consider the other equation,x-y=0.
Solve for y and you get y=x.
The coefficient of x is implied to be 1, which is the slope. There is nothing being added or subtracted from the x term, so the y-intercept is 0. Verify this by plugging in 0 for x. The y value is then x. By the same process, the x-intercept is also 0.
I hope this helps. Good luck.