Given:
[tex]\begin{gathered} x-intercept\text{ = }-\frac{2}{9} \\ y-intercept\text{ =1} \end{gathered}[/tex]Recall that we can write the intercepts as coordinates:
[tex]\begin{gathered} x-\text{intercept : (-}\frac{2}{9}\text{ , 0)} \\ y-\text{intercept }\colon\text{ (0, 1)} \end{gathered}[/tex]point-slope form:
The point-slope is defined as :
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m is the slope} \\ \text{and (x}_1,y_1)\text{ is the point} \end{gathered}[/tex]To find the point-slope formula, we use the formula:
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the given points:
[tex]\begin{gathered} \frac{y\text{ -}1}{x\text{ -0}}\text{ = }\frac{0-\text{ 1}}{-\frac{2}{9}\text{ -0}} \\ \frac{y-1}{x}\text{ = }\frac{-1}{-\frac{2}{9}} \\ \frac{y-1}{x}\text{ = }\frac{9}{2} \\ \text{Cross}-\text{Multiply} \\ 2(y-1)\text{ = 9x} \\ \text{Divide both sides by 2} \\ y\text{ - 1= }\frac{9}{2}x \\ y\text{ - 1 = }\frac{9}{2}(x-0) \end{gathered}[/tex]Answer:
[tex]y\text{ - 1 = }\frac{9}{2}(x-0)[/tex]Slope-intercept form
The slope intercept form is defined as:
[tex]\begin{gathered} y\text{ = mx + c} \\ \text{Where m is the slope and} \\ c\text{ is the intercept} \end{gathered}[/tex]Using the result from the point-slope form:
[tex]\begin{gathered} y\text{ - 1 = }\frac{9}{2}(x-0) \\ y\text{ - 1 = }\frac{9}{2}x \\ \text{Collect like terms} \\ y\text{ =}\frac{9}{2}x\text{ + 1} \end{gathered}[/tex]Answer:
[tex]y\text{ = }\frac{9}{2}x\text{ + 1}[/tex]