Question

A line is drawn on the coordinate plane that passes through the point $\left(10,1\right)$ and has a slope of $-0.5$. what is the $y-$intercept?

Answer 1

Find $y-$intercept of the line:

It is given that, a line passes through the point $\left(10,1\right)$ and has a slope$\left(10,1\right)$.

The slope-intercept form of the line is $y=mx+b$, where $\text{m}$ is the slope of the line, $\text{b}$ is the $y-$intercept and $\left(x,y\right)$ is the point on the line.

Substitute $\left(x,y\right)=\left(10,1\right)$ and $\text{m}=-0.5$ in $y=mx+b$:

$\begin{array}{rcl}y& =& mx+b\\ & \Rightarrow & 1=\left(-0.5\right)10+b\\ & \Rightarrow & 1=-5+b\\ & \Rightarrow & 6=b\end{array}$

Hence, the $y-$intercept of the line is $6$.