Question

Read the point slope form of the line’s equation satisfying the given conditions

Answer 1

The point-slope form

The point-slope form 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 given point} \end{gathered}`

Given:

Slope = 3

point : (6, 2)

Substituting the given value into the given formula:

`y\text{ - 2 = 3(x - 6)}`

Point-slope form:

y - 2 = 3(x - 6)

Slope-intercept form

The slope intercept form is defined as:

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

Simplifying the point-slope form, we get the slope-intercept form:

`\begin{gathered} y\text{ - 2 = 3(x - 6)} \\ y\text{ - 2 = 3x - 18} \\ \text{Collect like terms} \\ y\text{ = 3x - 18 + 2} \\ y\text{ = 3x - 16} \end{gathered}`

slope-intercept form:

y = 3x - 16