There are different methods to approach this:
1.. Form simultaneous equations based on y =mx + c
(Substitute the values of x and y which have been given.)
-34 = m(3) + c and -9 = m(4) + c
Solve them to find the values of m and c, which will give the equation of the line. Elimination by subtracting the 2 equations is probably the easiest as the c terms will subtract to 0.
2. Use the two points to find the gradient. m = (y_2 - y_1)/(x_2 - x_1)
Then substitute values for m and one point x, y into y =mx + c to find c.
Finally answer in the form y =mx + c, using the values for m and c you have found.
3. Use the formula from coordinate (or analytical) geometry which uses 2 points and a general point (x, y)
(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)
Substitute the values for the 2 given points, calculate the fraction on the right hand side (which gives the gradient), cross-multiply and with a small amount of transposing, the equation of the line is obtained.
(y - (-34))/(x - 3) = (-9 - (-34))/(4 - 3) = 25/1
(y+34)/(x-3) = 25/1 Now cross-multiply
y+34 = 25x-75
y = 25x -109
