Write an equation in slope-intercept form for the line that passes through (3,5) and (-2,1).
y2-y1/x2-x1
1-5/-2-3
-4/-5= slope
y=mx+b
y=-4/-5(3)+b
-2=2.4+b
-4.4= y-intercept
y= -4/-5x+4.4 (answer)
Rewrite the slope as m = 4/5. -4/-5 is the same thing but looks awkward.
y = (4/5) x + b
5 = [(4/5)*3] + b
5 = 12/5 + b
b = 13/5
y = (4/5)x + 13/5
Ok, we lmow that the slope is 4/5.
y=mx+b
y=4/5(3)+b
-2=2.4+b
subtract 2.4 from both sides
-4.4 which is how I got the y-intercept
y= 4/5x+4.4
13/5 = 2.6 not 4.4
In solving for b, you took the x-value from one point (x=3) and, for y, you used the x value from the other point (x=-2) instead of y. You should have used y=5, as I did in my derivation. You have to use the x and y values of one known point to get the line to pass though that point.
To find the equation in slope-intercept form for the line that passes through the points (3, 5) and (-2, 1), you can follow these steps:
Step 1: Find the slope (m) of the line using the formula: slope (m) = (y2 - y1) / (x2 - x1).
Substituting the coordinates, plugging in the values:
m = (1 - 5) / (-2 - 3) = -4 / -5 = 4/5.
Step 2: Use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Using the slope (m) we found in Step 1, the equation becomes:
y = (4/5)x + b.
Step 3: Find the y-intercept (b) by substituting one of the given points into the equation and solving for b.
Let's choose the point (3, 5):
5 = (4/5)(3) + b.
5 = 12/5 + b.
To get rid of the fraction, multiply both sides of the equation by 5:
25 = 12 + 5b.
Subtracting 12 from both sides:
13 = 5b.
Dividing both sides by 5:
b = 13/5 = 2.6.
So, the equation in slope-intercept form for the line passing through (3, 5) and (-2, 1) is:
y = (4/5)x + 2.6.