line cd passes through points c(1, 3) and d(4, -3). if the equation of the line is written in slope…
line cd passes through points c(1, 3) and d(4, -3). if the equation of the line is written in slope - intercept form, y = mx + b, what is the value of b? -5 -2 1 5
Answer
Explanation:
Step1: Calculate the slope $m$
The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $C(1,3)$ and $D(4, - 3)$, we have $x_1 = 1,y_1=3,x_2 = 4,y_2=-3$. Then $m=\frac{-3 - 3}{4 - 1}=\frac{-6}{3}=-2$.
Step2: Substitute a point and the slope into the equation $y=mx + b$
Substitute the point $C(1,3)$ and $m=-2$ into $y=mx + b$. We get $3=-2\times1 + b$.
Step3: Solve for $b$
First, simplify the right - hand side of the equation: $3=-2 + b$. Then add 2 to both sides of the equation: $b=3 + 2=5$.
Answer:
5