Question

What is the equation of the line that passes through the point (-3,1) andhas a slope of 2/3

Answer 1

The answer is very simple.

Step 01:

Data:

slope = m = 2/3

point (-3,1) x = -3 y = 1

Step 02:

Point-Slope Equation of a Line.

(y - y1) = m * (x - x1)

(y - 1 ) = 2/3 * (x - (-3))

`\begin{gathered} y\text{ - 1 = }\frac{2}{3\text{ }}(x\text{ +3) } \\ y\text{ - 1 = }\frac{2\text{ x}}{3}\text{ + }(6)/(3) \end{gathered}`
`\begin{gathered} y\text{ - 1 }=\text{ }(2)/(3)\text{ x + 2} \\ y\text{ -1-2 = }(2)/(3)x \\ y\text{ -3 = }(2)/(3)x \\ y\text{ = }(2)/(3)x\text{ + 3} \end{gathered}`

The solution is:

y = 2/3 x + 3