Question

Use the information provided y=2\5x-4 to find the correct matching graph

Answer 1

The equation of a line in slope-intercept form, is:

`y=mx+b`

Where m is the slope of the line and b is the y-intercept.

In the given equation:

`y=(2)/(5)x-4`

The slope is equal to 2/5 and the y-intercept is equal to -4.

Since the y-intercept is equal to -4, this means that the line must pass through the point (0,-4), since it cuts the y-axis at y=-4.

On the other hand, we can calculate the coordinates of another point on the line choosing a value for x and figuring out the corresponding value of y using the given equation.

For instance, let's see which value of y corresponds to x=5:

`\begin{gathered} y=(2)/(5)(5)-4 \\ =2-4 \\ =-2 \end{gathered}`

Then, the point (5,-2) must belong to the line.

On the graphs, search for one where the line passes throught the points (0,-4) and (5,-2):