Which of the following graphs represents the equation 𝑦 equals negative 𝑥 plus seven?
So we’ve been given five graphs, each with a different straight line drawn on it. And we’re asked to determine which of these represents the straight line whose equation is 𝑦 equals negative 𝑥 plus seven. To answer this, let’s consider the slope–intercept form of the equation of a straight line. It’s 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑚 represents the slope of the line and 𝑐 represents the 𝑦-intercept.
We can compare this general form with the equation that we’ve been given and determine the slope and 𝑦-intercept of our line. First of all, we know that the 𝑦-intercept of our line is seven. Now let’s look at the five graphs and, specifically, at the point where each of the lines crosses the 𝑦-axis. We can see the only lines A and D cross the 𝑦-axis at this point seven. The others cross at negative seven, negative one, or negative two.
For this reason, A and D are currently the only two possibilities remaining for the graph that represents 𝑦 equals negative 𝑥 plus seven. Now let’s consider the slope of the line. The coefficient of 𝑥 in our equation is negative one, which means the slope of the line is negative one. This means that the line slopes downward from left to right and for every one unit you move to the right, the line moves one unit down.
Looking at lines A and D, we can see that line A slopes upwards. It has a positive slope. Line D, however, does slope downwards. It has a negative slope. If we look at line D more closely, we can see that it does indeed have a slope of negative one. For every one unit we move to the right, the line moves one unit down.
Therefore, graph D has both the correct slope and the correct 𝑦-intercept. And therefore, graph D represents the equation 𝑦 equals negative 𝑥 plus seven.