Question

A line passes through the point (-6,4) and has a slope of 5/2. Write an equation in a slope intercept form for this line.

Answer 1

`\text{The equation of line: }y\text{ = }(5)/(2)x\text{ + 19}`

Step-by-step explanation:

The given point: (-6, 4)

slope of the line = 5/2

To get the equation of line in slope -intereot form, we will use the formula:

`\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}`

Since we already know the slope, we need to find the y-intercept

point (-6, 4): x = -6, y = 4

We will substitute the slope and the point in the formula above to get y-intercept:

`\begin{gathered} y\text{ = mx + b} \\ 4\text{ = }(5)/(2)(-6)\text{ + b} \\ 4\text{ = -15 + b} \\ 4\text{ + 15 = b} \\ b\text{ = 19} \end{gathered}`

The equation of line in slope intercept becomes:

`y\text{ = }(5)/(2)x\text{ + 19}`