23 Jun ##y = -2/3x + 2## By definition the x-intercept of 3 is the
##y = -2/3x + 2## By definition the x-intercept of 3 is the point (3 0) and By definition the y-intercept of 2 is the point (0 2). Because we have two points we can use the point- formula to determine the equation. In order to use the point-slope formula we must first determine the slope of the line. The slope can be found by using the formula: ##color(red)(m = (y_2 = y_1)/(x_2 – x_1)## Where ##m## is the slope and ##(x_1 y_1)## and ##(x_2 y_2)## are the two points. Substituting the two points from the problem gives the slope as: ##m = (0 – 2)/(3 – 0)## ##m = -2/3## Now that we have the slope we can use the point-slope formula to determine the equation of the line: The point-slope formula states: ##color(red)((y – y_1) = m(x – x_1))## Where ##m## is the slope and (x_1 y_1) is a point the line passes through. We can substitute the slope we calculated and one of the points to give: ##y – 0 = -2/3(x – 3)## ##y = -2/3x + 2/3 * 3## ##y = -2/3x + 2##
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