Question

I need help please and thank you and you have to graph it

Answer 1

From the graph provided we can determine two points which are;

`\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(2,0) \end{gathered}`

For the equation of the line given in slope-intercept form which is;

`y=mx+b`

We would begin by calculating the slope which is;

`m=(y_2-y_1)/(x_2-x_1)`

We can now substitute the values shown above and we'll have;

`\begin{gathered} m=((0-\lbrack-3\rbrack))/(2-0) \\ m=(0+3)/(2) \\ m=(3)/(2) \end{gathered}`

Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;

`\begin{gathered} y=mx+b \\ \text{Where;} \\ x=0,y=-3,m=(3)/(2) \end{gathered}`

We now have the equation as;

`\begin{gathered} -3=(3)/(2)(0)+b \\ -3=0+b \\ b=-3 \end{gathered}`

We now have the y-intercept as -3. The equation now is;

`\begin{gathered} \text{Substitute m and b into the equation,} \\ y=mx+b \\ y=(3)/(2)x-3 \end{gathered}`

The graph of this is now shown below;

We shall now draw lines to indicate the 'rise' and 'run' of this graph.

ANSWER

Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).

This clearly defines the slope of the equation that is;

`(\Delta y)/(\Delta x)=\frac{Change\text{ in y}}{Change\text{ in x}}=(3)/(2)`