Question 975075


As you know, the slope-intercept form is y = mx + b where m = slope and b is the y-intercept.


(a) Line contains the point (-3,5) and is perpendicular to the line y=3x-4

For the equation y = 3x - 4 our slope is perpendicular to the line so we will write m = -1/3 which is the inverse of 3. Next we apply the point-slope formula using our slope, m = -1/3 and points (x1, y1) or (-3,5):


y - y1 = m(x - x1)


y - (5) = -1/3(x - (-3))


y - 5 = -1/3(x + 3)


y - 5 = (-1/3)x - 1 --> y = (-1/3)x - 1 + 5


y = -(1/3)x + 4 and this is your equation in slope-intercept form.


Perpendicular: {{{y = (-1/3)x + 4}}}


(b) Line contains the point(2,3) and is parallel to 5x-y=10.


We have to put 5x -y = 10 in slope-intercept form first: 


-y = -5x + 10 --> dividing the equation by (-1) we change the signs to y = 5x - 10


Your slope is m = 5. Since parallel lines have identical slopes, the parallel line through point (2,3) will have slope m = 5.


Use the point-slope form in (a) to find the line using your slope m = 5 and point (2, 3).



y - y1 = m(x - x1)  --> y - 3 = 5(x - 2)


Solving, 


y - 3 = 5x - 10


Parallel: y = 5x - 7