Question

13. Write the equation of a line with a slope of 2/3, which goes through the point (6,1). Equation:

Answer 1

Given in the question:

a.) The slope of the line (m) = 2/3

b.) Point passing through the line, x,y = 6,1

In writing the equation, let's first determine the y-intercept (b) by substituting the value of the slope and the point 6,1 in the slope-intercept formula.

$\text{ y=mx + b}$

At m = 2/3 and x,y = 6,1

$\text{ y = mx + b }\rightarrow\text{ 1 = (}\frac{2}{3})(6)\text{ + b}$$\text{ 1 = }\frac{12}{3}\text{ + b }\rightarrow\text{ 1 = 4 + b}$$\text{ b = 1 - 4}$$\text{ b = -3}$

Let's now complete the equation by substituting the value of the slope (m) and the y-intercept (b) in the slope-intercept formula.

$\text{ y = mx }+\text{ b }\rightarrow\text{ y = (}\frac{2}{3})x\text{ + (-3)}$$\text{ y = }\frac{2}{3}x\text{ - 3}$

Therefore, the equation of the line is y=2x/3 - 3.