Find an equation of the line containing the given pair of points
(3,4) and (9,6)
I got 2/3x+2. is this right?
The slope is (6-4)/(9-3) = (1/3)
y = (x/3) + constant
4 = (3/3) + constant
the constant = 3
y = (x/3) + 3
Your answer is not right. You could have verified that by substitution. You also need to insert parentheses into what you wrote because it is not clear if you mean
2/(3x) + 2, or 2/(3x+2) or (2/3)x + 2
All three are wrong.
Please clarify. what is constant?
How did you get 3. Did you subtract 1 from 4?
yes.
4-1 = 3 is the constant
I got it by forcing the line of slope (1/3) to go through the point (3,4)
I would have got the same answer by forcing it to go through the other point, (9,6).
okay i tried this one. is this right?
(2,4)and (6,7)
the slope is (7-4)/(6-2)=2/1
y=(x/1)+constant
4=(1/1)+constant
the constant=2
y=(x/2)+2
If the slope is 1/2, how can the equation be y = (x/1)+ 1?
Your very first line is wrong
(7-4)/(6-2) does not = 2/1 = 2
The slope is 3/4
The next line also makes no sense. Where did the x/1 come from?
For your new example, the slope is (3/4)
The equation must fit
y = mx + b where m = 3/4, x = 2 and y = 4
4 = (3/4)*2 + b
b = 5/2
y = (3/4)x + 5/2
how did you get 5/2?
I did the math
4 = (3/4)*2 + b
b = 4 - 3/2 = 5/2
To find the equation of a line passing through two points, you can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 4) and (9, 6):
m = (6 - 4) / (9 - 3)
m = 2 / 6
m = 1/3
Now that we have the slope, we can use one of the given points and substitute the values into the equation y = mx + b to find the y-intercept (b). Let's use the point (3, 4):
4 = (1/3) * 3 + b
4 = 1 + b
b = 4 - 1
b = 3
Therefore, the equation of the line passing through the points (3, 4) and (9, 6) is:
y = (1/3)x + 3
So, your answer of 2/3x + 2 is not correct. The correct equation is y = (1/3)x + 3.