Equation of a line given a slope a point i.e sloape and one point form
Generally, equation of a line is given by y = mx + c
where m is slope and c is the intercept
to obtain the equation with the slope given and a point (x,y)
substitute for y,x and m to obtain the intercept then rewrite the equation
Question 1. (1 , 4) , m = 3. x=1,y=4
[tex]\begin{gathered} y\text{ = mx + c} \\ 4\text{ =}3\text{ }\times1\text{ + c} \\ 4\text{ = 3 + c} \\ 4-3\text{ = c} \\ 1=c \\ c\text{ =1} \\ \text{then the equation is } \\ y\text{ = 3x + 1} \end{gathered}[/tex]Question 2. ( - 2, 1) , m= - 2, x=-2 , y = 1
[tex]\begin{gathered} y\text{ = mx + c} \\ 1\text{ = -2}\times-2\text{ + c} \\ 1\text{ = 4 +c} \\ 1-4\text{ = c} \\ -3\text{ = c} \\ c\text{ =-3} \\ y=-2x\text{ + (-3)} \\ y\text{ = -2x -3} \end{gathered}[/tex]Question 3. (3, 5) , m = 1 , x=3, y= 5
[tex]\begin{gathered} y\text{ =mx + c} \\ 5\text{ = 1}\times3\text{ + c} \\ 5\text{ = 3 +c} \\ 5-3=c \\ 2\text{ = c} \\ c=2 \\ y\text{ = 1x + 2} \\ y\text{ = x +2 is the equation} \end{gathered}[/tex]Question 4. (2, -1) , m =1/2 . x=2 , y = -1
[tex]\begin{gathered} y\text{ = mx + c} \\ -1\text{ = 1 }\times\frac{1}{2}\text{ + c} \\ -1\text{ = }\frac{1}{2}\text{+c} \\ -1\text{ - }\frac{1}{2}\text{ = c} \\ c\text{ = -}\frac{3}{2} \\ \text{the equation is } \\ y=1x\text{ + }\frac{-3}{2} \\ y\text{ = x -}\frac{3}{2} \\ y\text{ = }\frac{2x\text{ -3}}{2} \\ 2y\text{ = 2x - 3} \end{gathered}[/tex]