How do I find 2 points on the line y=2/5x+4 and then use those points to find the slope?

Question

I was given a problem that says "Find two points of each line and then use those points to find the slope." Then given the following equation: y=2/5x+4. I tried using the method of substituting 0 for x and then 0 for y, but I come up with a different slope than the answer key.

Answer 1

Since the equation y=2/5x + 4 is provided to you, you can start where Kevin instructed you and find your y-intercept for the first point on the line. As he noted, to find the intercept, plug in 0 for x and you end up with y=4 so one point on your line should be (0,4). For simplicity's sake, the way I would solve the rest of the problem (to answer the teacher's question most directly) diverges. I would use the provided equation to solve for the x intercept, and I would make this point the second point of my line. To get the x intercept, plug in 0 for y and solve for x. x is equal to -10 and your x intercept should be (-10,0). Next I would plot the two points, draw a line between them and show that 2/5 is really the slope (remember that the m of y=mx+b is the variable representing slope) of the line you have drawn. You can do this by calculating the rise/run or y2-y1/x2-x1. When you plug in your coordinates for the points you plotted, you should have (4-0)/(0-(-10)) which is equal to 4/10 which is the same as 2/5. Thus you have proved, as the question indicated necessary, that the slope of the line (formed by the two points you plotted) is the same as the slope in the given equation y=2/5x+4.

hopefully, this response is helpful!

Answer 2

The origin (0,0) will not always be a point on the line. 

The y-intercept gives the y value when x = 0, so that's a starting point. 

What is the y-intercept? If the equation is in the form y = mx + b, then the value of b is the y-intercept. Since the formula is y = (2/5) x + 4, then the y intercept is 4 and the point is (0,4)

Now, pick at least one other x value (given the slope as 2/5, 5 might be a good option). Then plug it in and solve for the next y value. Although 2 points make a line, you can do three just to make sure.