Question

What is the slope and y-intercept of the line $y=-2x+8$?

Answer 1

Hint: For solving this question you should know about the slope of a line and the y-intercept of a line. If the point is given at x-axis, then we will see the change at that axis. If the change occurs there, then there will be a slope which we will count by calculations but if there is no change or $\Delta x=0$, then it has no slope and it never cuts the y-axis also. And if it has a slope, then use it to find them.

Complete step by step solution:
According to our question it is asked of us to find the slope and y-intercept of the line $y=-2x+8$. If we find the y-intercept then it is found where the line in question crosses the y-axis (vertical axis), or when our x in a coordinate point is 0, such as (0, y) the slope if found by the change in y/change in x.
The slope intercept form is $y=mx+b$ where m is the slope and b is the y-intercept. If we have to find the slope, take any two points along the line or two given. For example, (3, 6) and (5, 7). The change in y is going to be ${{y}_{2}}-{{y}_{1}}$ or in case of 7 - 6, which is equal to one. Then we calculate our change in x, which is done in a same way but with x variables: ${{x}_{2}}-{{x}_{1}}$ or in case of 5 - 3, it will be equal to 2.
Therefore, for example, our slope will be $\dfrac{\Delta y}{\Delta x}$ and here,
 $\Delta y={{y}_{2}}-{{y}_{1}}=1$
And,
$\Delta x={{x}_{2}}-{{x}_{1}}=2$
So, the slope is $\dfrac{1}{2}$.
But here the equation is given in the form of $y=mx+c$ and here the slope of the line is,
$\begin{align}
  & y=-2\left( x \right)+8 \\
 & \Rightarrow m=-2 \\
\end{align}$
So, the slope is -2.
And y-intercept refers to the value when $x$ equals to zero, then,
$\begin{align}
  & y=-2\left( 0 \right)+8 \\
 & y=0+8 \\
 & y=8 \\
\end{align}$
So, the slope is -2 and y-intercept is (0, 8).

Note: The y-intercept of any line occurs only when x intersects y. And if that is not intersecting or cutting to that then, it will not have any y-intercepts there. And if the change in x values of any equation of line is equal to zero then the slope of that line always has undefined values.