Question

Find an equation of the line that passes through the points (-3, 4) and (0, 7)

Answer 1

y = x + 7

Explanation:

Slope m = (y2-y1)/(x2-x1)

given (-3,4) and (0,7)

m = (7 - 4)/(0 - -3) = 3/3 = 1

Slope-intercept: y = mx + b

using (0,7)

7 = 1(0) + b

b = 7

then y = 1x + 7

y = x + 7

Answer 2

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{7}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}}\implies \cfrac{3}{0+3}\implies 1 \\\\\\ \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}{1}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-4=x+3\implies y=x+7`