Thank you Christina.. I am taking Algebra online...something I would never recommend....How would I write the equation of the line passing through (6,37) and (1,12)?
the most common way is to use y=mx + b
where m is the slope and b is the y-intercept
so the first thing you have to do is to find the slope, I will assume you know how to do that
m=(12-37)/(1-6)
=-25/-5
=5
Now pick the simpler looking of your two points, say (1,12) and substitute the x, the y and the m in your equation.
12 = 5(1) + b
so b =7 and your equation is
y = 5x+7
to test if this is right, use the point that was not used and replace its values in the equation.
Left side = 37
Right side = 5(6)+7 = 37
so we have the right equation
To write the equation of a line passing through two points (x1, y1) and (x2, y2), we can use the point-slope form of a linear equation: y - y1 = m(x - x1).
In this case, the two points are (6, 37) and (1, 12). To find the slope, use the formula: m = (y2 - y1) / (x2 - x1).
m = (12 - 37) / (1 - 6)
= -25 / -5
= 5
Now that we have the slope, we can choose either of the two points to substitute into the equation. Let's choose (1, 12):
y - 12 = 5(x - 1)
Next, simplify the equation:
y - 12 = 5x - 5
To isolate y, add 12 to both sides of the equation:
y = 5x - 5 + 12
= 5x + 7
So, the equation of the line passing through (6, 37) and (1, 12) is y = 5x + 7.
To verify if this equation is correct, we can substitute the other point, (6, 37), into the equation:
Left side: y = 37
Right side: 5(6) + 7 = 30 + 7 = 37
Since both sides are equal, we have the correct equation.