Question

The graph of a linear function is shown on the grid.
Which equation is best represented by this graph?
X
/
VE
y=
Submit
y-axis
10-
5
-10
-5
0
5
10
x-axis
-5
the points are at 4, 4 and -4, -2

Answer 1

To find the equation of the linear function represented by the points (4, 4) and (-4, -2), we first need to determine the slope (m) of the line.

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's assign the points as follows:
- Point 1: \( (4, 4) \) \( (x_1, y_1) \)
- Point 2: \( (-4, -2) \) \( (x_2, y_2) \)

Now applying the slope formula:

\[
m = \frac{-2 - 4}{-4 - 4} = \frac{-6}{-8} = \frac{3}{4}
\]

So the slope \( m = \frac{3}{4} \).

Next, we can use the point-slope form of a line to find the equation of the line. The point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Using the point (4, 4):

\[
y - 4 = \frac{3}{4}(x - 4)
\]

Now, we will distribute and rearrange to find the slope-intercept form (y = mx + b):

\[
y - 4 = \frac{3}{4}x - 3
\]

Adding 4 to both sides:

\[
y = \frac{3}{4}x + 1
\]

Thus, the equation of the line that best represents the graph is:

\[
y = \frac{3}{4}x + 1
\]