determine the slope, y intercept and x intercept

Question

determine the slope, x-intercept, and y-intercept of the following equations

x - y = 0

y = 3x - 5

Answer 1

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.