Geometry Fundamentals: Slope 6

Since the slope tells us the amount that the value of $y$ changes for any unit change in $x$ , and we can see that $(3, 39), (4, a)$ are one $x$ -unit apart, we can conclude that $a$ must be equal to $39$ plus the value of the slope, $10$ . Thus the answer is $39 + 10 = 49$ .

Alternately, we could use the formula for slope ( $m = \frac{y_2-y_1}{x_2-x_2}$ ), and substitute in all of the known values:

$10 = \frac{ a - 39}{ 4-3 },$

which also shows that $a = 49$ .

• We know that a straight line has equation $y = mx + c$ , hence

$39 = 10(3) +c \implies c = 9$

• To find $a$ , we just keep $f(x) = a$ since it is the y-cordinate

$a = 10(3) + 9 \implies \boxed{a = 49}$