Question

(-8,-8);parallel to -x+8y=16Write the equation of the line in standard & slope intercept form.

Answer 1

To write the equation of the given line:

1. Find the slope (m), use the parallel line as parallel lines have the same slope.

Write the equation of the parallel line in slope intercept form (y=mx+b) to identify the slope:

`\begin{gathered} -x+8y=16 \\ 8y=x+16 \\ y=(1)/(8)x+(16)/(8) \\ \\ y=(1)/(8)x+2 \end{gathered}`

Slope: 1/8

2. Use the given point and the slope to find the y-intercept (b):

`\begin{gathered} (-8,-8);x=-y,y=-8 \\ m=(1)/(8) \\ \\ y=mx+b \\ -8=(1)/(8)(-8)+b \\ \\ -8=-1+b \\ -8+1=b \\ \\ b=-7 \end{gathered}`

3. Write the equation in slope-intercept form:

`y=(1)/(8)x-7`

2. Leave the terms with variable in left side of the equal to write the equation in standard form:

`y-(1)/(8)x=-7`

_________

Answer:

Standard form: y - 1/8 x = -7

Slope-intercept form: y = 1/8 x - 7