Question

Find the equations of the lines in slope-intercept form that are parallel and perpendicular to the line 4x-3y=17 that pass through the point (12,7).

Answer 1

y= (4/3)x -9

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, x is the x coordinate and c is the y-intercept.

The property of two parallel lines is that they have the same gradient so if we arrange the 2nd line equation (4x-3y=17) into y= mx+c we can find the gradient of the first line.

4x-3y=17

3y= 4x - 17

y= (4/3)x - 17/3 (we have to write it in the form of y=mx+c)

This means that the gradient of the first line is 4/3

So y= (4/3)x + c

We don't have c but we can find c by plugging the coordinate in the form of (x,y), (12,7) into the equation and rearranging it to find c.

7= (4/3)×12 + c

7= 16 + c

c= 7-16= -9

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

y= (4/3)x -9