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;
[tex]y=mx+b[/tex]has the slope m as 2/3, and if it passes through the points (-3,1), then;
[tex]\begin{gathered} y=mx+b \\ 1=\frac{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=\frac{2}{3}x+3 \end{gathered}[/tex]A parallel line that passes through the point (-3, 1) is given by the equation;
y = 2/3x + 3
