Video Transcript
True or False: The equation of a
straight line with 𝑥-intercept two, zero and 𝑦-intercept zero, three is 𝑥 over
two plus 𝑦 over three equals one.
In this question, we’re given the
𝑥- and 𝑦-intercepts of a straight line and asked to determine if the given
equation is an equation of the line. There are many ways we can answer
this question. However, the easiest is to recall
the two-intercept form of the equation of a line. This tells us that if a line has
𝑥-intercept at 𝑎 and 𝑦-intercept at 𝑏 and does not pass through the origin, then
an equation of the line is 𝑥 over 𝑎 plus 𝑦 over 𝑏 equals one. We are given a line with distinct
intercepts, so we can substitute 𝑎 equals two and 𝑏 equals three into the
two-intercept form to obtain 𝑥 over two plus 𝑦 over three equals one. This is equivalent to the given
equation, so we can say that the answer is true.
