For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
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Answer:
Slope: 4
Y-intercept: -5
Equation: y=4x-5
Step-by-step explanation:
Slope formula:
So let's use the ordered pairs (1, -1) and (2,3) from the table (it doesnt matter which ones you choose) and plug the numbers in to the formula:
Which is equal to:
Which is equal to 4. So the slope is 4.
To find the y-intercept, substitute the slope and an ordered pair into the slope-intercept equation, y=mx+b. So let's use (1,-1).
-1=4(1)+b
= -1=4+b
= -1-4=4-4+b
= -5=b
So the y-intercept is -5.
Then for the equation, you just plug in the slope and the y-intercept into y=mx+b, which would be:
y=4x-5