Question

Find the equation of line b described below , in slope intercept form. Line a is parallel to line bLine a passes through the points (1,5) and (2,-7)Line b passes through the point (1,15)The equation of line b is

Answer 1

Parallel lines have the same slopes and different y-intercepts

We will find the slope of the parallel line, then take it as a slope of line b

The rule of the slope is

`m=(y2-y1)/(x2-x1)`

Where (x1, y1) and (x2, y2) are two points lie on the line

Since the parallel line passes through the points (1, 5), (2, -7), then

x1 = 1 and x2 = 2

y1 = 5 and y2 = -7

Substitute them in the rule above

`\begin{gathered} m=(-7-5)/(2-1) \\ m=(-12)/(1) \\ m=-12 \end{gathered}`

Since parallel lines have the same slope, then the slope of line b is -12

Since the slope-intercept form of the linear equation is

`y=mx+c`

Then the equation of line b is

`y=-12x+c`

To find c substitute x and y by the coordinates of any point lies on line b

Since line b is passed through the point (1, 15), then

x = 1 and y = 15

`\begin{gathered} 15=-12(1)+c \\ 15=-12+c \end{gathered}`

Add 12 to both sides to find c

`\begin{gathered} 15+12=-12+12+c \\ 27=c \end{gathered}`

Then the equation of line b is

`y=-12x+27`