Question

In your own words how you would explain slope to a struggling student and...

Answer 1

From the given graph

To find the slope of a given line, we pick two points from the graph and use their x and y coordinates to find the slope as shown below

Where

`\begin{gathered} x=0,y=-4 \\ (x_1,y_1)\Rightarrow(0,-4) \\ x=6,y=5 \\ (x_2,y_2)\Rightarrow(6,5) \end{gathered}`

To find the slope of a line, the formula is

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

Substitute the coordinates into the formula above

`\begin{gathered} (y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ (y-(-4))/(x-0)=(5-(-4))/(6-0) \\ (y+4)/(x)=(5+4)/(6) \\ (y+4)/(x)=(3)/(2) \end{gathered}`

Crossmultiply

`\begin{gathered} 2(y+4)=3(x) \\ 2y+8=3x \\ 2y=3-8 \\ Divide\text{ both sides by 2} \\ (2y)/(2)=(3x-8)/(2) \\ y=(3)/(2)x-4 \end{gathered}`

Hence, the equation of the given line in the slope-intercept form is

`y=(3)/(2)x-4`