Question

The equation of a straight line is y=5x+7

Write down the gradient of the line and the coordinates of the y-intercept.

Answer 1

bearing in mind that the slope goes by several names

average rate of change

rate of change

deltaY over deltaX

rise over run

gradient

constant of proportionality

however, is the same cat wearing different hats.

`\bf y = \stackrel{\stackrel{m}{\downarrow }}{5}x+\stackrel{\stackrel{b}{\downarrow }}{7}\qquad \impliedby \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hfill \begin{cases} \stackrel{gradient}{slope}=&5\\ y-intercept=&(0,7) \end{cases}`