# How do you graph the line #y = -1/3x - 7#?

See a solution process below:

First, solve for two points which solve the equation and plot these points:

We can next plot the two points on the coordinate plane:

graph{(x^2+(y+7)^2-0.075)((x-3)^2+(y+8)^2-0.075)=0 [-20, 20, -15, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{(y + (1/3)x + 7)(x^2+(y+7)^2-0.075)((x-3)^2+(y+8)^2-0.075)=0 [-20, 20, -15, 5]}

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To graph the line y = -1/3x - 7, plot the y-intercept at (0, -7), which is where the line crosses the y-axis. Then, use the slope of -1/3 to find another point. Since the slope is -1/3, this means that for every increase of 3 units to the right, the line goes down by 1 unit. So, from the y-intercept (0, -7), move 3 units to the right and 1 unit down to get the next point, and so on. Drawing a line through these points will represent the graph of y = -1/3x - 7.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Points A and B are at #(3 ,6 )# and #(7 ,3 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(1 ,-8 )# and point B is at #(-3 ,-2 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Circle A has a radius of #2 # and a center at #(3 ,1 )#. Circle B has a radius of #4 # and a center at #(8 ,3 )#. If circle B is translated by #<-2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A triangle has corners at #(8 ,3 )#, #(4 ,-5 )#, and #(-7 ,-4 )#. If the triangle is dilated by a factor of #5 # about point #(1 ,-3 ), how far will its centroid move?
- Point A is at #(2 ,-4 )# and point B is at #(1 ,8 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

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