What would the equation be of a straight line that passes through the points (1,1) and (3,3) ??
write the equation for the line:
y= mx+ b
put the first set of points in..
1=1m + b then the second equation
3=3m + b subtract the equations...
2=2m so you know m.
Put that into either equation and solve for b.
i don't quite understand what you mean .
will m = 1 ??
so that would mean b = 0 ?
yes, slope is 1
so would the equation would be (1,0) ?
sorry i mean y = 1 x 1 + 0 ??
Actually, let's go through the process step by step to find the equation for the line passing through the points (1,1) and (3,3).
1. Recall that the equation for a straight line is in the form of y = mx + b, where m represents the slope of the line and b is the y-intercept.
2. Substitute the coordinates of the first point, (1,1), into the equation. This gives us the equation 1 = 1m + b.
3. Substituting the coordinates of the second point, (3,3), into the equation gives us 3 = 3m + b.
4. Subtracting the two equations will eliminate the b term: (3 - 1) = (3m - 1m) + (b - b). This simplifies to 2 = 2m.
5. Divide both sides of the equation by 2 to solve for m: 2/2 = 2m/2, which gives us 1 = m.
6. Now, substitute the value of m, which is 1, back into one of the original equations. Let's use the equation 1 = 1m + b. This becomes 1 = 1(1) + b.
7. Solve for b by simplifying the equation: 1 = 1 + b. Subtracting 1 from both sides gives us b = 0.
8. Now we know that the slope (m) is 1 and the y-intercept (b) is 0, so the equation for the line passing through the given points is y = 1x + 0, which simplifies to y = x.
Therefore, the equation of the straight line passing through the points (1,1) and (3,3) is y = x.