Use two points on the line to find the equation of the line

Use two points on the line to find the equation of the line, in standard form.

Solution

Let us select two points where the line in the given graph meets the X -Axis and the Y -AXIS. These points are ( 5, 0) and ( 0, - 2) respectively. Let the equation of the line be y = mx + c where m is the slope and c is the y -intercept. On substituting x = 0 and y = -2 in this equation, we get - 2 = m(0) + c or, c = -2 ( even otherwise, we can see from the graph that the y-intercept, i.e. the y-value,when x = 0, is -2 so that c = -2). Then the equation of the line changes to y = mx - 2. On substituting x = 5 and y = 0 in this equation, we get 0 = m(5) - 2 or, 5m = 2 so that m = 2/5. Then the equation of the line changes to y = (2/5)x - 2. The slope of the line is 2/5