line mn passes through points m(4, 3) and n(7, 12). if the equation of the line is written in slope…

Explanation:

Step1: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(4,3)$ and $(x_2,y_2)=(7,12)$, then $m=\frac{12 - 3}{7 - 4}=\frac{9}{3}=3$.

Step2: Substitute a point and slope into $y=mx + b$

Substitute $m = 3$, $x = 4$, and $y = 3$ into $y=mx + b$. We get $3=3\times4 + b$.

Step3: Solve for $b$

First, simplify the right - hand side: $3 = 12 + b$. Then subtract 12 from both sides: $b=3 - 12=-9$.

Answer:

-9