Question

7x + 10?
(-4, 2)
(2, -4)
b) (5, 25)
d) (10, 0)
that passes through the point (-4, -5)
12)
graph of f(x) as a line on a grid
a) what is f(5)?
b) for which value of x does f(x)=2?

Explanation:

Step1: Determine the equation of the line

First, find the slope \( m \) using two points on the line. From the graph, we can see that the line passes through \((0, -2)\) (y-intercept) and let's take another point, say \((2, -4)\). The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). So \( m = \frac{-4 - (-2)}{2 - 0} = \frac{-2}{2} = -1 \). The equation of the line in slope - intercept form \( y = mx + b \) is \( y=-x - 2 \), so \( f(x)=-x - 2 \).

Step2: Calculate \( f(5) \)

Substitute \( x = 5 \) into the function \( f(x)=-x - 2 \). So \( f(5)=-5 - 2=-7 \)? Wait, maybe my initial point selection is wrong. Let's re - examine the graph. Looking at the grid, when \( x = 0 \), \( y=-2 \) (y - intercept). Let's take another point: when \( x = 5 \), we can count the grid. Wait, maybe a better way: from the graph, the line has a slope of - 1 (since for every 1 unit increase in x, y decreases by 1). Wait, let's check the intersection with x - axis: when \( y = 0 \), \( 0=-x - 2\Rightarrow x=-2 \). Wait, maybe I made a mistake. Let's look at the graph again. Let's take two clear points: (0, -2) and ( - 2, 0). Then the slope \( m=\frac{0 - (-2)}{-2 - 0}=\frac{2}{-2}=-1 \). So the equation is \( y=-x - 2 \). Now, for part a) \( f(5) \): substitute \( x = 5 \) into \( y=-x - 2 \), we get \( y=-5 - 2=-7 \)? Wait, but maybe the graph is different. Wait, looking at the graph, when x = 5, let's count the grid. Each square is 1 unit. Starting from (0, -2), moving 5 units to the right (x = 5) and 5 units down (since slope is - 1), so y=-2-5=-7.

For part b) We need to find x when \( f(x) = 2 \). Set \( -x - 2=2 \). Solve for x: \( -x=2 + 2=4\Rightarrow x=-4 \). Wait, let's check the graph. If \( f(x) = 2 \), we look for the y - value of 2 on the y - axis, then find the corresponding x - value on the line. Moving left from the y - axis, since the slope is - 1, when y increases by 4 (from - 2 to 2), x decreases by 4 (from 0 to - 4). So \( x=-4 \).

Wait, maybe my initial equation is wrong. Let's re - evaluate the graph. Let's take two points: (0, -2) and (2, -4). The slope is \( \frac{-4+2}{2 - 0}=\frac{-2}{2}=-1 \), equation \( y=-x - 2 \).

Part (a)

Step1: Correct the equation (maybe I misread the graph)

Wait, looking at the graph again, maybe the y - intercept is - 2? Wait, no, let's count the grid. Let's take the point (0, -2) and ( - 2, 0). So the line goes through ( - 2, 0) and (0, -2). So the slope is \( m=\frac{-2 - 0}{0 - (-2)}=\frac{-2}{2}=-1 \), equation \( y=-x - 2 \). So for \( x = 5 \), \( f(5)=-5 - 2=-7 \).

Part (b)

Step1: Solve for x when \( f(x)=2 \)

Set \( f(x)=2 \), so \( -x - 2 = 2 \). Add 2 to both sides: \( -x=4 \), multiply both sides by - 1: \( x=-4 \).

Answer:

a) \( f(5)=-7 \)

b) \( x = - 4 \)