Write the equation of a line that goes through (5,3) and (2,7)
I found the slope of the line to be -4/3
Then, I substituted one of the points in for x and y to be:
y = -4/3x + b
3 = -4/3(5) + b
3 = -20/3 + b
3 + 20/3 = b
This is where I am stuck == do I have to find the common denominator, so I end up with 29/3 as my b?
So then my equation is y = -4/3x + 29/3?
yes
Yes, you are on the right track. To find the value of b, you need to simplify the expression 3 + 20/3. To do that, you can find the common denominator between 3 and 20/3, which is 3.
To express 3 as a fraction with a denominator of 3, you can multiply both the numerator and denominator by 3:
3 = 3/1
Now, you can add the fractions:
3/1 + 20/3 = (3 * 3)/3 + 20/3 = 9/3 + 20/3 = 29/3
So, the value of b is 29/3. Therefore, the equation of the line passing through (5,3) and (2,7) is:
y = (-4/3)x + 29/3