SOLUTION: Find a point M on the line y= -2x + 3 such that the slope of the line through (2,3) and M is equal to 2

Question 911751: Find a point M on the line y= -2x + 3 such that the slope of the line through (2,3) and M is equal to 2
Found 2 solutions by jim_thompson5910, lwsshak3:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
All points on y = -2x+3 are of the form (x,y) = (x, -2x+3)

(x1,y1) = (2,3)
(x2,y2) = (x, -2x+3)

Slope formula

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

2 = (-2x+3 - 3)/(x - 2)

2 = (-2x)/(x - 2)

2(x - 2) = -2x

2x - 4 = -2x

-4 = -2x - 2x

-4 = -4x

-4x = -4

x = (-4)/(-4)

x = 1

--------------

y = -2x+3

y = -2(1)+3

y = -2+3

y = 1

So the point M is (1,1)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find a point M on the line y= -2x + 3 such that the slope of the line through (2,3) and M is equal to 2
***
Equation of a line: y=mx+b, m=slope, b=y-intercept
y=mx+b
using coordinates of given point on the line(2,3) and slope=2
3=2*2+b
b=-1
equation:
y=2x-1
y=-2x+3(given)
add:
2y=2
y=1
2x=y+1
2x=2
x=1
point of intersection, M:(1,1)

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