Slope intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Slope can be found by choosing two points (x₁, y₁) and (x₂, y₂) and calculating the change in y over the change in x. As a formula,
[tex] m = \frac{y_{2}- y_{1}}{x_{2}-x_{1}} [/tex]
For question 3, we choose (0, 1.5) and (100, 36.5) as our points. You can choose any pair - but you must be consistent in choosing from the x and y group and not to cross your choices. Don't take (0, 36.5). Let (0, 1.5) be the (x₁, y₁) pair, and (100, 36.5) the (x₂, y₂ pair).
So, m = (36.5 - 1.5) / (100 - 0)
m = 35 / 100 = 0.35
Next we take that slope and choose one of our points (0, 1.5). We let m = 0.35, x = 0 and y = 1.5, and solve for b in the slope intercept form.
y = mx + b
1.5 = (0.35)(0) + b
1.5 = 0 + b
1.5 = b
Thus, the y - intercept is 1.5. Now we finish it off and report the equation of the line with m = 0.35 and the y-intercept of 1.5
y = 0.35x + 1.5
Question 4 is done in the same manner. Choose (25, 94) for (x₁, y₁) and (35, 88) for (x₂, y₂).
m = (88 - 94) / (35 - 25)
m = -6 / 10 = -0.6
Choose m = -0.6, x = 25, y = 94, and solve for b.
94 = (25)(-0.6) + b
95 = -15 + b
110 = b
So the equation of the line here is y = -0.6x + 110.
