Question

Write the slope intercept form of the equation of th line trogh the given points. please

Answer 1

- The question would like us to write the equation of the line passing through the points (0, -2) and (5,5) in slope-intercept form.

- The slope-intercept form of a linear equation is given by:

`y=mx+c`

- The formula for solving this question is given below:

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ \text{where,} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates given} \end{gathered}`

- The coordinates given are (0, -2) and (5,5)

- Thus, we can solve the question as follows

`\begin{gathered} x_1=0,y_1=-2 \\ x_2=5,y_2=5 \\ \\ (y-(-2))/(x-0)=(5-(-2))/(5-0) \\ \\ (y+2)/(x)=(5+2)/(5) \\ \\ (y+2)/(x)=(7)/(5) \\ \\ \text{ Multiply both sides by }x \\ \\ y+2=(7x)/(5) \\ \\ \text{Subtract 2 from both sides} \\ \\ y=(7)/(5)x-2 \\ \\ \text{This is in the form }y=mx+c,\text{ where,} \\ m=(7)/(5)\text{ and }c=-2 \end{gathered}`

Final Answer

`y=(7)/(5)x-2`