Question

Please help if you can.Can you do 4 b) and c)

Answer 1

The equation of a line in its slope-intercept form is

$\begin{gathered} y=mx+b \\ \text{ Where m is the slope of the line and } \\ b\text{ is the y-intercept} \end{gathered}$

Then, to find the slope and the y-intercept of the given lines, you just have to take the equations to their slope-intercept form.

For point 4 b) you have

$\begin{gathered} 5x-10y=20 \\ \text{ Subtract 5x from both sides of the equation} \\ 5x-10y-5x=20-5x \\ -10y=20-5x \\ \text{ Divide by -10 into both sides of the equation} \\ \frac{-10y}{-10}=\frac{20-5x}{-10} \\ y=-\frac{20}{10}-\frac{5x}{-10} \\ y=-2+\frac{1}{2}x \\ \text{ Reordering} \\ y=\frac{1}{2}x-2 \end{gathered}$

Therefore, the slope and the y-intercept of this equation are

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

For point 4 c) you have

$\begin{gathered} x+2y=4 \\ \text{ Subtract x from both sides of the equation} \\ x+2y-x=4-x \\ 2y=4-x \\ \text{ Divide by 2 into both sides of the equation} \\ \frac{2y}{2}=\frac{4-x}{2} \\ y=\frac{4}{2}-\frac{x}{2} \\ y=2-\frac{1}{2}x \\ \text{ Reordering} \\ y=-\frac{1}{2}x+2 \end{gathered}$

Therefore, the slope and the y-intercept of this equation are

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