Graphing Linear Functions in Slope-Intercept Form

Equations in slope-intercept form follow a specific format. $$y=mx+b$$ In the above formula, $m$ represents the slope and $b$ the $y\text{-}$intercept of the line. The line has a slope of $\text{-}3,$ which means that we can substitute $\text{-}3$ for $m.$ $$y=mx+b\Rightarrow y=\text{-}3x+b$$ To write a complete equation for this line, we also need to determine the $y\text{-}$intercept, $b.$ We can do this by substituting the given point, $(1,4),$ into the equation and solving the resulting equation for $b.$ Now that we have both the slope and the $y\text{-}$intercept, we can write the equation. $$y=\text{-}3x+7$$