A line has slope –5/3 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 answer, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line.
Given that the slope of the line is -5/3, we can substitute this value for m in the equation:
y = (-5/3)x + b
To find the value of b, we can substitute the coordinates of one of the given points into the equation and solve for b. Let's use the point (11, 13):
13 = (-5/3)(11) + b
13 = -55/3 + b
To add -55/3 to both sides, we need to find a common denominator for 13 and -55/3, which is 3:
39/3 = -55/3 + b
39 + 55 = -165 + b
94 = b
Now that we know the value of b is 94, we can write the equation of the line as:
y = (-5/3)x + 94
Now we can check if the other given point (8, 18) satisfies this equation:
18 = (-5/3)(8) + 94
18 = -40/3 + 94
To add -40/3 to both sides, we need to find a common denominator for 18 and -40/3, which is 3:
54/3 = -40/3 + 94
54 + 40 = 270/3 + 94
94 = 94
Since both points satisfy the equation, the line with a slope of -5/3 passes through the points (11, 13) and (8, 18).