Question

Write an equation of a line that goes through the point (2,2) and has a y-intercept of 6

Answer 1

so the line goes through 2,2, and the y-intercept, well, a y-intercept is when the graph touches or "intercepts" the y-axis, and when that happens, x = 0, so the point is x = 0, y = 6, or 0,6, therefore


`\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ &&(~ 2 &,& 2~) &&(~ 0 &,& 6~) \end{array} \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{6-2}{0-2}\implies \cfrac{4}{-2}\implies -2 \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-2(x-2) \\\\\\ y-2=-2x+4\implies y=-2x+6`