What is the slope of a line if it passes through the points (0, 0) and (3, 6)?
1. Find the y-intercept of the line.
2. Write an equation for the line using your answers.
3. Find one more point that lies on the line.
4. Explain why that point is also a solution to the function.
Please explain your answers for better understanding. Thank you!
Answer (3)
very simple.
so slope=rise/run so if we plot the points and find how high and how long it went we see that the slope=6/3=2 slope=2
since the line goes through the origin (0,0) the y-intercept=(0,0) and the equation is y=mx+b m=slope b=how much away from the origin whic is not applicable in this problem. so y=2x
To find the slope you do the method Y2-Y1
X2-X1 So you do 6-0=6 and 3-0=3. That would be 6/3 and then, you simplify it. Your slope is 2. To find the y-intercept you have to do the point slope form, then, you do the slope intercept form Y-Y1=m(x-x1) You do y-6=2(x-3) Y-6=2x+(-6) You add six to both sides The equation is y=2x The y-intercept is -6 One more point on the line would be (4,8). Because if you look at the slope it is 2/1. When plotting a point you look at the slope as rise over run. The two is the rise and the 1 is the run. So you go to (3,6) and add 1 to the 3. Then, you add 2 to the 6 to get (4,8). That's why that point is a solution to the function. You could also do (2,4) if you did the opposite and subtracted the 2 and 1 to make the bottom half of the line.
The slope of the line through points (0, 0) and (3, 6) is 2, and the y-intercept is 0. The equation of the line is y = 2 x . Another point on the line is (1, 2), which also satisfies the equation, confirming it is part of the line.
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