Question

Write an equation of the line that passes through each points (5,6) (3.4)

Answer 1

Answer:

$y = x + 1$.

Step-by-step explanation:

Start by finding the slope of this line.

If a slanting line goes through $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$, where $x_{0} \ne x_{1}$, the slope of this line would be:

$\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}$.

The line in this question goes through $(5,\, 6)$ and $(3,\, 4)$. Hence, the slope of this line would be:

$\begin{aligned}m &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{6 - 4}{5 - 3} \\ &= 1\end{aligned}$.

If a slanting line with a slope of $m$ and goes through the point $(x_{0},\, y_{0})$, the equation of this line in the point-slope form would be:

$y - y_{0} = m,\, (x - x_{0})$.

For the line in this question, the slope is $m = 1$. Take $(5,\, 6)$ as the chosen point on this line. The point-slope form equation of this line would be:

$y - 6 = (x - 5)$.

Rewrite to obtain the equation of this line in the slope-intercept form:

$y = x + 1$.