Question

Question 2 Give the equation of a line that goes through the point (-8,6) and is perpendicular to the line -4x+3y=6. Give your answer in slope intercept form

Answer 1

y=
`(-1)/(4/3)`x +0

Explanation:

To find the equation of the line using the slope-intercept form we have to use the equation y=mx+c where y is the y coordinate and m is the gradient (slope), x is the x coordinate and c is the y-intercept.

The property of perpendicular lines is that their gradient is negative reciprocal meaning the equation would be y= (-1/m)x + c.

Now we can find m using the equation of the other line so first arrange it in y= (-1/m)x + c. form.

3y= 4x + 6

y= (4/3)x + 2

y=
`(-1)/(4/3)`x +2

We don't have c but we can find c by plugging the coordinate in the form of (x,y), (-8,6) into the equation and rearranging it to find c.

6=
`(-1)/(4/3)`(-8) + c

6= 6 +c

c= 0

Now remove the x and y and plug the value of c in there and you will get the equation.

y=
`(-1)/(4/3)`x +0