Question

Which equation represents the line that passes through ( -8, 11) and ( 4, 7/2)?

Answer 1

Answer:

A

Step-by-step explanation:

Recall the general equation for a straight line is

y = mx + b

where m is the gradient and b is the y-intercept

given 2 points whose coordinates are (x1, y1) and (x2, y2), m can be found with the following formula:

m = $\frac{y1-y2}{x1-x2}$

in this case, x1 = -8, y1 = 11, x2 = 4, y2=7/2

applying these values to the formula for m will give

m = -(5/8)

We can see immediately that the only 2 possible answers are A or B.

If we substitute this back into the general equation, we get:

y = -(5/8)x + b

In order to find the value for b, we substitute any one of the 2 given points back into this equation. Lets choose (-8,11)

11 = -(5/8) (-8) + b

11 = -(5/8) (-8) + b

11 = 5 + b

b = 6

hence A is the answer.