Question

Which equations and/or functions represent the graphed line? Select four options. f(x) = 0.2x - 4

f(x) = 0.5x + 2

f(x) = 1/2x + 2

y – 3 = 1/2(x – 2)

y – 1 = 0.5(x + 2)

Answer 1

first off, let's notice something on this line, the graph touches the y-axis at 2, namely when x = 0, y = 2, so that's the y-intercept for this line.

now, let's notice something else, as the line moves from x = -4, to the right towards x = 0, the run is 4 units, the rise is 2 units, so its slope is rise/run or 2/4 or 1/2, that said, that gives us an equation of

`\bf y=\cfrac{1}{2}x+2\qquad \impliedby \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\implies y=0.5x+2`

`\bf y-3 = \cfrac{1}{2}(x-2)\implies y-3=\cfrac{1}{2}x-1\implies y=\cfrac{1}{2}x+2\qquad \textit{\Large\checkmark} \\\\\\ y-1=0.5(x+2)\implies y-1=0.5x+1\implies y=0.5x+2\qquad \textit{\Large\checkmark} \\\\\\ f(x) = 0.2x-4\qquad \bigotimes`

Answer 2

f(x) = 0.2x - 4 (incorrect)

f(x) = 0.5x + 2 (correct)

f(x) = 1/2x + 2 (correct)

y – 3 = 1/2(x – 2) (correct)

y – 1 = 0.5(x + 2)

Explanation:

Step 1 : Find two coordinates

(0, 2) (-4, 0)

Step 2 : Find the slope

Slope = m = Y2-Y1/X2-X1

m = 0-2/-4-0

m = -2/-4

m = 1/2 or 0.5

Step 3 : Find the y-intercept

Y-intercept is where the line intersects the y-axis

c = 2

Step 4 : Form the equation y=mx + c

Given Equations and their slope intercept forms:

1) f(x) = 0.2x - 4

This is incorrect because slope is 1/2 or 0.5 and y intercept is 2

2) f(x) = 1/2x + 2

y = 1/2x + 2

This is correct because slope is 1/2 or 0.5 and y intercept is 2

3) f(x) = 0.5x + 2

y= 0.5x + 2 (As m=0.5)

This is correct because slope is 1/2 or 0.5 and y intercept is 2

4) y – 3 = 1/2(x – 2)

Rearranging in slope intercept form:

y-3=1/2x - 1

y = 1/2x-1+3

y = 1/2x + 2

This is correct because slope is 1/2 or 0.5 and y intercept is 2

5) y – 1 = 0.5(x + 2)

y -1 = 0.5x+1

y = 0.5x +1+1

y = 0.5x + 2

This is correct because slope is 1/2 or 0.5 and y intercept is 2

!!