Question

Use the given conditions to write an equation for the line in point slope intercept form

Answer 1

Given:

`\begin{gathered} x-intercept\text{ = }-(2)/(9) \\ y-intercept\text{ =1} \end{gathered}`

Recall that we can write the intercepts as coordinates:

`\begin{gathered} x-\text{intercept : (-}(2)/(9)\text{ , 0)} \\ y-\text{intercept }\colon\text{ (0, 1)} \end{gathered}`

point-slope form:

The point-slope is defined as :

`\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}`

To find the point-slope formula, we use the formula:

`(y-y_1)/(x-x_1)\text{ = }(y_2-y_1)/(x_2-x_1)`

Substituting the given points:

`\begin{gathered} \frac{y\text{ -}1}{x\text{ -0}}\text{ = }\frac{0-\text{ 1}}{-(2)/(9)\text{ -0}} \\ (y-1)/(x)\text{ = }(-1)/(-(2)/(9)) \\ (y-1)/(x)\text{ = }(9)/(2) \\ \text{Cross}-\text{Multiply} \\ 2(y-1)\text{ = 9x} \\ \text{Divide both sides by 2} \\ y\text{ - 1= }(9)/(2)x \\ y\text{ - 1 = }(9)/(2)(x-0) \end{gathered}`

Answer:

`y\text{ - 1 = }(9)/(2)(x-0)`

Slope-intercept form

The slope intercept form is defined as:

`\begin{gathered} y\text{ = mx + c} \\ \text{Where m is the slope and} \\ c\text{ is the intercept} \end{gathered}`

Using the result from the point-slope form:

`\begin{gathered} y\text{ - 1 = }(9)/(2)(x-0) \\ y\text{ - 1 = }(9)/(2)x \\ \text{Collect like terms} \\ y\text{ =}(9)/(2)x\text{ + 1} \end{gathered}`

Answer:

`y\text{ = }(9)/(2)x\text{ + 1}`