Question

If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value

of the slope and the values of x and y using the coordinates of the given point, then determine the value of b.
Using the above technique, find the equation of the line containing the points (-4,13) and (2,-2)

Answer 1

`y\text{ = -}(5)/(2)x\text{ + 3}`

Explanation:

Given the following coordinate points (-4, 13) and (2, -2)

The standard form of the slope-intercept equation is written below

`y\text{ = mx + b}`

Where

m = slope of the line

b = intercept of the y-axis

The next thing is to find the slope

The formula for slope is given below as

`\begin{gathered} \text{slope = }\frac{rise\text{ }}{\text{run}} \\ \text{rise = y2 - y1} \\ \text{run = x2 - x1} \\ \text{Slope = }\frac{y2\text{ - y1}}{x2\text{ - x1}} \end{gathered}`

According to the given points, we can deduce the following

x1 = -4

y1 = 13

x2 = 2

y2 = -2

Substitute the following data into the above formula

`\begin{gathered} \text{Slope = }\frac{-2\text{ - 13}}{2\text{ - (-4)}} \\ \text{Slope = }\frac{-15}{2\text{ + 4}} \\ \text{Slope = }(-15)/(6) \\ \text{Slope = }(-5)/(2) \end{gathered}`

The slope-intercept form of a given point

`\begin{gathered} (y\text{ - y1) = m(x - x1)} \\ y1\text{ = 13, and x1 = -4} \\ m\text{ = }(-5)/(2) \\ (y\text{ - 13) = }(-5)/(2)(x\text{ + 4)} \\ y\text{ - 13 = }(-5)/(2)\cdot\text{ x -}(5)/(2)\cdot\text{ 4} \\ y\text{ - 13 = -}(5)/(2)x\text{ - }(20)/(2) \\ y\text{ - 13 = -}(5)/(2)x\text{ - 10} \\ \text{Add 13 to the both sides} \\ y\text{ - 13 + 13 = -}(5)/(2)x\text{ - 10 + 13} \\ y\text{ = -}(5)/(2)x\text{ + 3} \end{gathered}`

Hence, the equation of the coordinate point

`y\text{ = -}(5)/(2)x\text{ + 3}`