Question

which of the graphs represents the line with the following slope and y-intercept:$m = \frac{1}{2} \: b = - 2$

Answer 1

$\begin{gathered} m=\frac{1}{2} \\ b=-2 \end{gathered}$

The equation of the line in the slope-intercept form is given by:

$\begin{gathered} y(x)=mx+b \\ so\colon \\ y(x)=\frac{1}{2}x-2 \end{gathered}$

The graph of this line is given by:

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$\begin{gathered} y=mx+b \\ (-4,0) \\ (0,3) \\ m=\frac{3-0}{0-(-4)}=\frac{3}{4} \end{gathered}$

so, using the point slope equation:

$\begin{gathered} y-(0)=\frac{3}{4}(x-(-4)) \\ y=\frac{3}{4}(x+4) \\ y=\frac{3}{4}x+3 \end{gathered}$

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Let:

$\begin{gathered} y=3x+2 \\ m1=3 \end{gathered}$

If 2 lines are parallel, then:

$m1=m2$

where m2 is the slope of the other line, so:

$\begin{gathered} m2=3 \\ let\colon \\ (x1,y1)=(1,3) \end{gathered}$

Using the point-slope equation:

$\begin{gathered} y-y1=m(x-x1) \\ y-3=3(x-1) \\ y-3=3x-3 \\ y=3x-3+3 \\ y=3x \end{gathered}$