Question

How do you interpret the slope and $y$-intercept $?$

Answer 1

Finding slope and $y$-intercept:

Slope:

Slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line. To calculate the slope of a line, we find a ratio that compares the change in $y$ (the rise) to the corresponding change in $x$(the run).

$y$-intercept:

A $y$-intercept of a graph is the $y$-coordinate of a point where the graph intersects the $y$-axis. The $x$-coordinate corresponding to a $y$-intercept is always zero.

If the equation of a non-vertical line is given in general form, it is possible to find the slope, $m$, and the $y$-intercept, $b$, for the line. We solve the equation for $y$, transforming it into the slope-intercept form $y=mx+b$. In this form, the coefficient of $x$ is the slope of the line and the constant term is its $y$-intercept.

For example : find the slope and the $y$-intercept of the line whose equation is $3x+2y-4=0$.

$\begin{array}{rcl}3x+2y-4& =& 0\\ y& =& \frac{-3x}{2}+2\end{array}$

On comparing with slope-intercept form $y=mx+b$

The slope of the line is $\frac{-3}{2}$ and the $y$-intercept is $2$.

Hence, the slope of the line is $m$ and the $y$-intercept is $b$.