Question

2. Write an equation in slope-intercept form of the line that passes through the point (-5, 7) and is perpendicular to the line y = 5x-1.

Answer 1

The general slope intercept form equation of a line is as stated below;

`y=mx+b`

where m is the slope and b is the intercept.

If we compare the given equation y = 5x-1 with the equation of a line, we can deduce that the slope, m, is 5.

The slope of a line perpendicular to another is always given as -1/m, therefore the line perpendicular to the line y=5x-1 will have a slope of -1/5;

So let's go ahead and substitute m= -1/5, into the point slope equation to determine the line that passes through (-5,7);

Remember, the point slope form equation of a line is given as;

`y-y_1=m(x-x_(1))`

Substituting the above values, we'll have

`y-7=-(1)/(5)(x+5)`

Let's open up the parenthesis first, we'll have;

`\begin{gathered} y-7=-(1)/(5)x-(5)/(5) \\ y-7=-(1)/(5)x-1 \end{gathered}`

Let's isolate y by adding 7 to both sides of the equation;

`y=-(1)/(5)x+6`

The above equation is the required equation of the line in slope intercept form which can be compared to the one earlier written above(y = mx + b).