A line has slope –The fraction negative five thirds.. Through which two points could this line pass? answer (11, 13), (8, 18)
how do you get the answer
To find the equation of a line that passes through two points, you can use the slope-intercept form of a line: y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope of the line is -5/3, you can substitute this value for m in the equation. Let's use the point (11, 13) to find the y-intercept:
13 = (-5/3)(11) + b
Multiply -5/3 by 11:
13 = -55/3 + b
To isolate b, add 55/3 to both sides:
13 + 55/3 = b
To simplify the right side, convert 13 to a fraction with a denominator of 3:
13 = 39/3
Adding 39/3 and 55/3 gives:
13 + 55/3 = 128/3 = b
So, the y-intercept is b = 128/3.
Now, you have the slope and the y-intercept, so the equation of the line passing through (11, 13) is:
y = (-5/3)x + 128/3.
You can repeat the same process for the second point (8, 18) to verify that the equation of the line is correct.