Question

Question #59258

Answer 1

See the entire solution explanation below.

Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

For this problem:

`y = color(red)(10)x + color(blue)(100)`

Therefore:

The slope is: `color(red)(m) = 10`

The y-intercept is: `color(blue)(b = 100)` or `(0, 100)`

To find the x-intercept, set `y` equal to `0` and solve for `x`:

`0 = color(red)(10)x + color(blue)(100)`

`0 - 100 = color(red)(10)x + color(blue)(100) = 100`

`-100 = color(red)(10)x + 0`

`-100 = color(red)(10)x`

`-100/10 = (color(red)(10)x)/10`

`-10 = (cancel(color(red)(10))x)/color(red)(cancel(color(black)(10)))`

`-10 = x`

`x = -10`

Therefore:

The x-intercept is: `x = -10` or `(-10, 0)`

Answer 2

y-int = (0, 100)
slope = 10
x-int = (-10, 0)

Explanation:

To find the Y-intercept of a line when it is written in Y-intercept form like it is above, you look at the number without the variable, if you want a technical answer you find it by setting `x=0` and solving for y which would give you 100 in either case.

The slope is found by looking at the coefficient of the x term which in this case is 10.

To find the X-intercept, do the opposite of what you did to find the Y-intercept and set y equal to 0 and solve for x like follows:

`0 = 10x + 100`

Get the terms with x alone on one side and the terms without x on the other side as such

`-100 = 10x`

And get x by itself by dividing both sides by 10 to get the answer

`-10 = x`