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

line $mn$ passes through points $m(4,3)$ and $n(7,12)$. if the equation of the line is written in slope - intercept form, $y = mx + b$, what is the value of $b$?\n-15\n-9\n3\n9

line $mn$ passes through points $m(4,3)$ and $n(7,12)$. if the equation of the line is written in slope - intercept form, $y = mx + b$, what is the value of $b$?\n-15\n-9\n3\n9

Answer

Explanation:

Step1: Calculate the slope $m$

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

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

Substitute $m = 3$ and the point $M(4,3)$ into $y=mx + b$. So $3=3\times4 + b$.

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