Question

i need help with question 3. how to find slope and all of that. we learned at as change in y/change in x. simple explanation please

Answer 1

So, the slope is in fact a change in y divided by a change in x:

`m=(\Delta y)/(\Delta x)`

To get this change, we can choose two points in the line.

In this case, we can pick the points marked, (0, -5) and (3, -1).

The change in y will be the difference between the y values. It is important to use the points in the same order to calculate the change in y and in x. so let's denote:

Point 1 - (0, -5)

Point 2 - (3, -1)

Let's see the difference from Point 1 to Point 2:

`\begin{gathered} \Delta y=y_2-y_1=-1-(-5)=-1+5=4 \\ \Delta x=x_2-x_1=3-0=3 \end{gathered}`

So, the slope is:

`m=(\Delta y)/(\Delta x)=(4)/(3)`

The y-intercept is the y-value in which the line intersects the y-axis, the vertical one. We can see that this happens at exaclty the point (0, -5), so the y-intercept is y = -5.

The line equation in the slope-intercept form is:

`y=mx+b`

Where m is the slope and b is the y-intercept. We already saw that:

`\begin{gathered} m=(4)/(3) \\ b=-5 \end{gathered}`

So, the equation is:

`y=(4)/(3)x-5`