# How do you find the intercepts and graph the line -8x +10=-40 x-intercept: y-intercept?

Jun 9, 2017

x-intercept: $x = 6.25$
The y-intercept does not exist

#### Explanation:

The x-intercept is the value of $x$ when $y = 0$
(this is just another way of saying that it is the value of $x$ where the equation crosses the X-axis, since for all points on the X-axis $y = 0$)

Given
color(white)("XXX")-8x+10=-40color(white)("XXX")"for all values of "y" including "y=0
$\Rightarrow - 8 x = - 50$

$\Rightarrow x = 6.25$

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The y-intercept is the value of $y$ when $x = 0$ (or, if you prefer the value of $y$ where the equation crosses the Y-axis)
....but setting $x = 0$ in the given equation implies $10 = - 40$
which is clearly impossible,
....or, from a graphic point of view, $- 8 x + 10 = 40$ is a vertical line (parallel to the Y-axis and therefore does not cross the Y-axis.

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