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Equations in slope-intercept form follow a specific format.
$y=mx+b$
In the above formula, $m$ represents the slope and $b$ the $y-$intercept of the line. The line has a slope of $-3,$ which means that we can substitute $-3$ for $m.$
$y=mx+b⇒y=-3x+b$
To write a complete equation for this line, we also need to determine the $y-$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 $y-$intercept, we can write the equation.
$y=-3x+7$

$y=-3x+b$

$4=-3⋅1+b$

MultiplyMultiply

$4=-3+b$

AddEqn$LHS+3=RHS+3$

$7=b$

RearrangeEqnRearrange equation

$b=7$