Question #59258

Mar 14, 2017

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: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

For this problem:

$y = \textcolor{red}{10} x + \textcolor{b l u e}{100}$

Therefore:

The slope is: $\textcolor{red}{m} = 10$

The y-intercept is: $\textcolor{b l u e}{b = 100}$ or $\left(0 , 100\right)$

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

$0 = \textcolor{red}{10} x + \textcolor{b l u e}{100}$

$0 - 100 = \textcolor{red}{10} x + \textcolor{b l u e}{100} = 100$

$- 100 = \textcolor{red}{10} x + 0$

$- 100 = \textcolor{red}{10} x$

$- \frac{100}{10} = \frac{\textcolor{red}{10} x}{10}$

$- 10 = \frac{\cancel{\textcolor{red}{10}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}$

$- 10 = x$

$x = - 10$

Therefore:

The x-intercept is: $x = - 10$ or $\left(- 10 , 0\right)$

Mar 14, 2017

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:

$0 = 10 x + 100$

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

$- 100 = 10 x$

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

$- 10 = x$