Question

Write an equation of the slope intercept form of the line passing through the points (2,3) and (4.6).

Answer 1

Hint: In the above given question, use the given points to find the slope of the equation and also find the y-intercept. Both these values so obtained can be substituted in the slope-intercept equation which is the $m = \dfrac{{6 - 3}}{{4 - 2}}$required solution.
We know that the slope of line passing through two points$\left( {{x_1},{y_1}} \right)$and$\left( {{x_2},{y_2}} \right)$is
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ … (1)$\left( {4,6} \right)$
So, the slope of the line passing through the points$\left( {2,3} \right)$and can be obtained by using $\therefore m = \dfrac{3}{2}$equation (1),

Complete step-by-step answer:
Therefore, the slope of the line is$\dfrac{3}{2}.$
Now use the slope and point (2,3) to find the y-intercept.
We know that
$y = mx + b$ … (2)
Therefore, after substituting the values in the equation (2), we get,
$ \Rightarrow 3 = \left( {\dfrac{3}{2} \times 2} \right) + b$
$ \Rightarrow 3 = 3 + b$
$ \Rightarrow b = 3 - 3$
$\therefore b = 0$
Now, after substituting the values of the slope and the intercept in the slope-intercept form, we get the equation as,
$y = mx + b$
$ \Rightarrow y = \dfrac{3}{2}x + 0$
$ \Rightarrow y = \dfrac{3}{2}x$
Hence, the equation of the line is$y = \dfrac{3}{2}x.$

Note: In order to solve the above given question, an adequate knowledge about lines and equations is required. Various equations like equation of slope, y-intercept, slope- intercept must be known. After substituting the given values in these equations, the required answer can be obtained.