Question

Which linear function is represented by the graph?

Answer 1

Answer-

Linear function that is represented by the graph is $y=-\dfrac{1}{2}x+1$

Solution-

From the graph,

y - intercept of the linear function is 1 and there are two points on the line (-4, 3), (4, -1)

We can get the equation of line by applying slope-intercept formula,

Slope of the line,

$=\dfrac{y_2-y_1}{x_2-x_1}\\\\=\dfrac{-1-3}{4+4}\\\\=\dfrac{-4}{8}\\\\=-\dfrac{1}{2}$

Now applying slope-intercept formula,

$y=mx+c$

Putting the values,

$\Rightarrow y=-\dfrac{1}{2}x+1$

$y=-\dfrac{1}{2}x+1$

Therefore, linear function that is represented by the graph is $y=-\dfrac{1}{2}x+1$

Answer 2

Answer:

option B is correct.

$y =\frac{1}{2}(-x)+1$

Step-by-step explanation:

Using Point slope form:

The equation of line is given by:

$y-y_1=m(x-x_1)$         .....[1]

where m is the slope of the line and $(x_1, y_1)$ is the point on the coordinate plane.

Consider any two points from the graph:

Let (0, 1) and (4, -1)

Calculate slope:

Slope is given by:

$m = \frac{y_2-y_1}{x_2-x_1}$

then substitute the given values we have;

$m = \frac{-1-1}{4-0}=\frac{-2}{4}=-\frac{1}{2}$

Now, substitute the value of m and (0, 1) in [1]  then;

$y-1=-\frac{1}{2}(x-0)$

Simplify:

$y-1=-\frac{1}{2}x$

Add 1 to both sides we have;

$y =\frac{1}{2}(-x)+1$

Therefore, the linear function is represented by the graph is

$y =\frac{1}{2}(-x)+1$