Question

Write the equation of line that passes through the points (-1,4) and (3,6)

Answer 1

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{ 2 }{3 +1} \implies \cfrac{ 2 }{ 4 } \implies \cfrac{1}{2}`

`\begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{(-1)}) \implies y -4 = \cfrac{1}{2} ( x +1) \\\\\\ y-4=\cfrac{1}{2}x+\cfrac{1}{2}\implies y=\cfrac{1}{2}x+\cfrac{1}{2}+4\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x+\cfrac{9}{2} \end{array}}`

Answer 2

y - y1 = m(x - x1)
y - 4 = (1/2)(x - (-1))
y - 4 = (1/2)(x + 1)

Simplify:

y - 4 = (1/2)x + 1/2

Rearrange the equation to slope-intercept form (y = mx + b), where b is the y-intercept:

y = (1/2)x + 1/2 + 4
y = (1/2)x + 9/2

Therefore, the equation of the line passing through the points (-1, 4) and (3, 6) is y = (1/2)x + 9/2.