# Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= 4x + 2 The function g(x) going through 0, −2 and 1, 3 The function f(x) has a larger slope. The function g(x) has a larger slope. They both have the

## Below are two different functions, $f \left(x\right) \mathmr{and} g \left(x\right)$. What can be determined about their slopes? $f \left(x\right) = 4 x + 2$ The function $g \left(x\right)$ going through (x,y)=(0, −2) and (x,y)=(1, 3) The function $f \left(x\right)$ has a larger slope. The function $g \left(x\right)$ has a larger slope. They both have the same slope. The relationship between slopes cannot be determined.

Jun 23, 2018

$f \left(x\right) = 4 x + 2$, $g \left(x\right) = 5 x - 2$
Therefore $g \left(x\right)$ has a larger slope.

#### Explanation:

The slope is the constant in front of x, i.e. f(x) has a slope of 4

The way I understand your statement, you mean that g(x) goes through the points (0, -2) and (1, 3) (otherwise one might understand your statement that g(x) is, 0, -2, 1, 3 for some values of x).

From this it follows that $g \left(0\right) = - 2$ and $g \left(1\right) = 3$,
i.e. $g \left(x\right)$ increases (has a slope of) $3 + 2 = 5$ when x increases fro 0 to 1.

Therefore g(x) has a greater slope than f(x).

If we write g(x)=ax+b
we have $a \cdot 0 + b = - 2$ => $b = - 2$
$a \cdot 1 - 2 = 3$ => $a = 5$
Therefore, $g \left(x\right) = 5 x - 2$

Jun 23, 2018

$g \left(x\right)$ has the 'greater' slope

#### Explanation:

The slope of $f \left(x\right)$ is such that it 'goes up' 4 for 1 along.

Lets have a look at $g \left(x\right)$

The slope (gradient) is determined by reading along the x-axis from left to right. Thus using $x$ the left most point ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(0 , - 2\right)$ and the right most point ${P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(1 , 3\right)$

For the slope we have

${P}_{2} - {P}_{1} = \left(\text{change in y")/("change in x}\right) = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{3 - \left(- 2\right)}{1 - 0} = \frac{5}{1} = 5$

$g \left(x\right) \to 5$
$f \left(x\right) \to 4$
Thus $g \left(x\right)$ has the 'greater' slope