Can you please help me understand this? Thanks
Find the value of y so that the passing line through the two points has the given slope.
1. (2,y) (3,3) ;m=2
Two-point form of linear equation :
y - y1 = ( y2 - y1 ) * ( x - x1 ) / ( x2 - x1 )
Add y1 to both sides
y - y1 + y1 = ( y2 - y1 ) * ( x - x1 ) / ( x2 - x1 ) + y1
y = ( y2 - y1 ) * ( x - x1 ) / ( x2 - x1 ) + y1
Alope-intercept form of linear equation :
y = m x + b
In this case :
x1 = 2
y1 = y
x2 = 3
y2 = 3
m = ( y2 - y1 ) / ( x2 - x1 ) = 2
( 3 - y ) / ( 3 - 2 ) = 2
( 3 - y ) / 1 = 2
3 - y = 2 Subtract 2 to both sides
3 - y - 2 = 2 - 2
1 - y = 0 Add y to both sides
1 - y + y = 0 + y
1 = y
y = 1
just find the slope for the two points, set it equal to 2
(y-3)/(2-3) = 2 --- (y-3)/-1 = 2
y-3 = -2
y = 1
Sure! To find the value of y that makes the line passing through the points (2, y) and (3, 3) have a slope of 2, we can use the slope formula.
The slope formula is:
m = (y2 - y1) / (x2 - x1)
Let's plug in the values from the given points into the slope formula:
2 = (3 - y) / (3 - 2)
Now we can solve for y by cross-multiplying:
2(3 - 2) = 3 - y
6 - 4 = 3 - y
2 = 3 - y
Next, we isolate y by subtracting 3 from both sides of the equation:
2 - 3 = -y
-1 = -y
Finally, we solve for y by multiplying both sides by -1:
1 = y
Therefore, the value of y that makes the line passing through the points (2, y) and (3, 3) have a slope of 2 is y = 1.