Solution
- 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:
[tex]y=mx+c[/tex]- The formula for solving this question is given below:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{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}[/tex]- The coordinates given are (0, -2) and (5,5)
- Thus, we can solve the question as follows
[tex]\begin{gathered} x_1=0,y_1=-2 \\ x_2=5,y_2=5 \\ \\ \frac{y-(-2)}{x-0}=\frac{5-(-2)}{5-0} \\ \\ \frac{y+2}{x}=\frac{5+2}{5} \\ \\ \frac{y+2}{x}=\frac{7}{5} \\ \\ \text{ Multiply both sides by }x \\ \\ y+2=\frac{7x}{5} \\ \\ \text{Subtract 2 from both sides} \\ \\ y=\frac{7}{5}x-2 \\ \\ \text{This is in the form }y=mx+c,\text{ where,} \\ m=\frac{7}{5}\text{ and }c=-2 \end{gathered}[/tex]Final Answer
[tex]y=\frac{7}{5}x-2[/tex]