Question

The equation y=mx+b goes through the points (4,-1) and (-8,-7)What’s the value of m What’s the value of b

Answer 1

The equation of a straight line given two points (4, -1) and (-8, -7) can be found using the formula:

`\begin{gathered} (y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \\ \text{where the points are:} \\ (x_1,y_1)=(4,-1) \\ (x_2,y_2)=(-8,-7) \end{gathered}`

Put the coordinate points into the formula,

`\begin{gathered} (-7-(-1))/(-8-4)=(y-(-1))/(x-4) \\ (-7+1)/(-12)=(y+1)/(x-4) \\ (-6)/(-12)=(y+1)/(x-4) \\ \text{simplify the fraction} \\ (1)/(2)=(y+1)/(x-4) \\ \text{cross multiply,} \\ 2(y+1)=x-4 \\ \text{divide through by 2,} \\ (2(y+1))/(2)=(x-4)/(2) \\ y+1=(x)/(2)-(4)/(2) \\ \text{simplify the fraction} \\ y+1=(1)/(2)x-2 \\ \text{collect like terms} \\ y=(1)/(2)x-3 \end{gathered}`

Comparing the equation of the line obtained with the formula y = mx + b:

`\begin{gathered} y=mx+c \\ y=(1)/(2)x-3 \\ On\text{ comparing,} \\ m=(1)/(2) \\ c=-3 \end{gathered}`

Therefore, m= 1/2, c = -3