Question

write each equation in slope-intercept form.21. y -6 =-2(x + 2)24. y -8 = 3(x + 5)27.y-1/2=x+1/2

Answer 1

The slope-intercept form is given by

$y=mx+b_{}$

Where m is the slope, b is the y-intercept.

Let us convert the given equations into the slope-intercept form.

$y-6=-2\mleft(x+2\mright)$

Expand the parenthesis on the right and then separate the y variable on the left side.

$\begin{gathered} y-6=-2x-4 \\ y=-2x-4+6 \\ y=-2x+2 \end{gathered}$

Similarly, repeat the above process for the 2nd equation

$\begin{gathered} y-8=3\mleft(x+5\mright) \\ y-8=3x+15_{} \\ y=3x+15+8_{} \\ y=3x+23 \end{gathered}$

Finally, the 3rd equation

$\begin{gathered} y-\frac{1}{2}=x+\frac{1}{2} \\ y=x+\frac{1}{2}+\frac{1}{2} \\ y=x+1 \end{gathered}$

Therefore, the equations in the slope-intercept form are

$\begin{gathered} 21.\: \: y=-2x+2 \\ 24.\: \: y=3x+23 \\ 27.\: \: y=x+1 \end{gathered}$