Respuesta :
Step 1
Given; Line m passes through points (1, 2) and (-3, -4). What is the equation of the line parallel to line m that passes through point (0,5)?
Step 2
We will find the slope of line m
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ slope=\frac{-4-2}{-3-1}=-\frac{6}{-4}=\frac{3}{2} \end{gathered}[/tex]Step 3
What is the equation of the line parallel to line m that passes through point (0,5)?
Parallel lines have the same slope. Thus
[tex]m_1=m_2=\frac{3}{2}[/tex]The equation of a line in slope-intercept form is;
[tex]\begin{gathered} y=mx+b \\ y=\frac{3}{2}x+b \\ b=y-intercept \\ y=5,x=0 \end{gathered}[/tex]Thus, the y-intercept of the required line will be;
[tex]\begin{gathered} 5=\frac{3}{2}(0)+b \\ b=5 \end{gathered}[/tex]The answer will be;
[tex]\begin{gathered} y=1.5x+5 \\ or \\ y=\frac{3}{2}x+5 \end{gathered}[/tex]