If the line y = mx + c passes through the points (2, -4) and (-3, 1), determine the values of m and c.

Equation of line passing through (2, -4) and (-3, 1) i.e. two points can be given by two-point formula i.e.

$\Rightarrow y - y$1 = \dfrac{y2 - y1}{x2 - x1}(x - x1) \\[1em] \therefore y - (-4) = \dfrac{1 - (-4)}{-3 - 2}(x - 2) \\[1em] \Rightarrow y + 4 = \dfrac{5}{-5}(x - 2) \\[1em] \Rightarrow y + 4 = -1(x - 2) \\[1em] \Rightarrow y + 4 = -x + 2 \\[1em] \Rightarrow y = -x - 2.

Comparing the above equation with y = mx + c we get,

m = -1 and c = -2.

Hence, the value of m is -1 and c is -2.