How can I work out the equation of a line defined by 2 known points?
We know that the equation of a line takes up the slope-intercept form: y = mx + n,where m is the slope and n is the y intercept To work out the equation of the line for our 2 points, we use the point-slope formula: y - y1 = m(x - x1)where m is the slope and x1 and y1 are the coordinates of a point on the line.In our case, we know that A (5, 2) is a point on the line so x1 = 5 and y1 = 2.In order to use the point-slope formula, we also need to work out the slope of the line. We know that the slope has the formula: m = change in y/change in x = yB - yA/ xB - xA,where xA and yA represent the coordinates of point A, in our case, xA = 5 and yA = 2.and, similarly, xB and yB represent the coordinates of point A, in our case, xB = 1 and yB = 6.We substitute the values that we know in the formula above to work out the slope.=> m = 6 - 2/ 1 - 5=> m = 4/-4=> m = -1 We work out the equation of the line by using m, x1 and y1 in the point-slope formula: y - y1 = m(x - x1)y - 2 = -1(x - 5)We simplify this equation, putting it in the form: y = mx + n=> y - 2 = -x + 5=> y = -x + 7 The equation of the line is: y = -x + 7.
