Question

The given set of points lie on the graph of a linear function.
Points: $(-3,-17),(-1,-9),(0,-5),(1,-1)$

Which of the following coordinates do not lie on the graph of the function described above?

• A. $(3,7)$
• B. $(5,11)$
• C. $(2,3)$
• D. $(4,11)$

Answer 1

The correct option is B $(5,11)$

Given,
$(-3,-17),(-1,-9),(0,-5),\text{and}(1,-1)$ are the points that lie on the graph of a linear function.

We know that, in a linear function, the slope is constant for any two points on the line.

The slope between the first and the second points $=\frac{\left(\right(-9)-(-17\left)\right)}{(-1)-(-3)}=\frac{-9+17}{-1+3}=\frac{8}{2}=4$

So, the slope between any two points on the line must be equal to $4$.

Option A: $(3,7)$
The slope between the point given in option $A$ and the first point $=\frac{\left(\right(-17)-7)}{(-3)-3}=\frac{-24}{6}=\frac{24}{6}=4$

Option B: $(4,11)$
The slope between the point given in option $B$ and the first point $=\frac{\left(\right(-17)-11)}{(-3)-4}=\frac{-28}{-7}=\frac{28}{7}=4$

Option C: $(2,3)$
The slope between the point given in option $C$ and the first point $=\frac{\left(\right(-17)-3)}{(-3)-2}=\frac{-20}{-5}=\frac{20}{5}=4$

Option D: $(5,11)$
The slope between the point given in option $A$ and the first point $=\frac{\left(\right(-17)-11)}{(-3)-5}=\frac{-28}{-8}=\frac{28}{8}=3.5$

Hence, the point $(5,11)$ do not lie on the graph of the function described above.

Option D is correct.