### Video Transcript

Write the equation represented by the graph shown. Give your answer in the form ๐ฅ plus ๐ฆ equals ๐.

So weโve been given a diagram of a coordinate grid and a line whose equation weโre asked to find. Weโre going to approach this question by finding both, the slope and the ๐ฆ-intercept of this line. And then we may need to do some algebraic rearranging of our answer in order to bring it into the requested form.

So letโs look carefully at the diagram, first of all. We can see the coordinates of the points at which the line cuts both, the ๐ฅ- and ๐ฆ-axes. In fact, it cuts both axes at a value of five. Weโll be able to use these two points to find both, the slope and the ๐ฆ-intercept of our line. So we begin with the equation of our line in slope-intercept form, ๐ฆ equals ๐๐ฅ plus ๐.

Letโs look at finding the value of ๐, first of all. From the diagram, we can see that the line cuts the ๐ฆ-axis at a value of five. And therefore, ๐ is equal to five. We can substitute this value ๐ into the equation of our line. So we have ๐ฆ is equal to ๐๐ฅ plus five.

Next, we need to calculate the slope of the line, ๐. Given the coordinates of two points on the line, the slope can be calculated as ๐ฆ two minus ๐ฆ one divided by ๐ฅ two minus ๐ฅ one. So letโs look carefully at the two points we know and determine their coordinates. The point where the line crosses the ๐ฆ-axis has an ๐ฅ-coordinate of zero, and so the coordinates of this point are zero, five. The point where the line crosses the ๐ฅ-axis has a ๐ฆ-coordinate of zero, and so the coordinates of this point are five, zero.

Now we can substitute these values into our calculation of the slope of the line. Remember, it doesnโt matter which point we refer to as ๐ฅ one, ๐ฆ one and which we refer to as ๐ฅ two, ๐ฆ two. Iโve chosen purely at random to think of the two points in this order. So the slope then, first of all, ๐ฆ two minus ๐ฆ one, this is zero minus five. Then I need to divide by ๐ฅ two minus ๐ฅ one which is five minus zero. This simplifies to negative five over five which is just equal to negative one.

So now weโve calculated the slope of the line. We can substitute this value of ๐ into our equation. So we have ๐ฆ is equal to negative ๐ฅ plus five. Remember in algebra, when we have a coefficient of one or negative one, we donโt write one ๐ฅ or negative one ๐ฅ; we just write ๐ฅ or negative ๐ฅ.

Now weโve nearly finished, but if we look back at the question, we see that we were asked for our answer in a specific format, ๐ฅ plus ๐ฆ is equal to ๐. So in order to bring my answer into this format, thereโs just one more step. I need to add ๐ฅ to both sides of this equation.

And having done so, I now have our answer to the problem: ๐ฅ plus ๐ฆ is equal to five.