Question

Write an equation of a line in slope- intercept form that is parallel to the line represented by y=2/3x+1

Answer 1

The line given is written in slope-intercept form as;

y=2/3x + 1

The slope is 2/3 and the y-intercept is 1. For a parallel line with the same slope (parallel lines on a coordinate grid have the same slope), we shall take the y-intercept at another point.

The line expressed as;

`y=mx+b`

has the slope m as 2/3, and if it passes through the points (-3,1), then;

`\begin{gathered} y=mx+b \\ 1=(2)/(3)(-3)+b \\ 1=-2+b \\ 1+2=b \\ 3=b \\ \text{When a parallel line passes through the point (-3, 1),} \\ \text{The y-intercept (b) becomes 3, therefore the equation is;} \\ y=mx+b \\ y=(2)/(3)x+3 \end{gathered}`

A parallel line that passes through the point (-3, 1) is given by the equation;

y = 2/3x + 3