Question

How do you find the slope of $\left( 0,0 \right), \left( 3,5 \right)$?

Answer 1

The slope of a line passing through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is given by the formula $m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$. Then by substituting the values of points in the formula and simplifying the obtained equation we will get the desired answer.

Complete step-by-step solution:
We have been given the points $\left( 0,0 \right), \left( 3,5 \right)$.
We have to find the slope of a line passing through the given points.
We know that slope of a line is the ratio of the difference of y-coordinate to x-coordinate for the given two points. The value of slope may be positive, negative or zero.
Now, we know that the slope of a line passing through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is given by the formula $m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$. When one point is $\left( 0,0 \right)$, it means the line starts from the origin.
Now, we have ${{x}_{1}}=0,{{y}_{1}}=0,{{x}_{2}}=3,{{y}_{2}}=5$
Now, substituting the values in the formula we will get
$\Rightarrow \dfrac{5-0}{3-0}$
Now, simplifying the above obtained equation we will get
$\Rightarrow \dfrac{5}{3}$
Hence we get the slope of a line passing through the points $\left( 0,0 \right), \left( 3,5 \right)$ is $\dfrac{5}{3}$.

Note: The equation of slope-intercept form of the line is given as $y=mx+c$, where m is the slope of the line and c is the y-intercept of the line. We can also find the equation of a line by using the formula $\dfrac{y-{{y}_{1}}}{x-{{x}_{1}}}=\dfrac{{{y}_{1}}-{{y}_{2}}}{{{x}_{1}}-{{x}_{2}}}$ or $\left( y-{{y}_{2}} \right)=\left( \dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)\left( x-{{x}_{2}} \right)$ passing through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$.