Write the equation of the line graphed below in Point-Slope form. Use the point labeled on the graph. State the slope and point.

Answer (point): (-1,1)

Explanation (point): In this graph, the point is indicated by a dot on the line. We can turn this into a coordinate by understanding the format of (x,y). This means that to turn the point into a coordinate, we need to find where it lands on the x-axis, and then find where it lies on the y-axis. In this case, it is -1 and 1. This means our point is (-1,1).

Answer (slope): -6

Explanation (slope): To find the slope, we need to follow the formula of rise/run. This means that we will choose two points, and find the difference between them in height and length. Let’s use (-1,1) and (0,-5). For these points, the distance in height is 6, and the distance in length is 1. This would make the slope 6/1, which can be reduced to 6. This will not be the final slope, however, since we need to add a negative sign before it. The negative sign will be used since the line on the graph declines. This makes the slope -6.

Answer (equation): y= -6x-5

Explanation (equation): The final thing we need to do is find the equation. We will do this last, as it uses some of the information we already discovered. Let’s start by writing out the formula for slope- intercept form. This is y=mx+b. In this equation y and x remains the same, while m and b will be the variables we change. Let’s begin with m, which stands for the slope. This is something we have already determined is -6, so we can substitute this in now. The equation is now
y= -6x+b. Let’s now change b. B stands for the y-intercept, which is the point where the line crosses the y- axis. In this case, it is -5. Let’s add this into the equation now to finalize it. Our equation will be y= -6x-5.

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