A line has a slope of 2 and contains the points (1, 3) and (2, y). The value of y is what?
Please explain in detail
Use the slope formula.
m = (x2-x1)/(y2-y1)
2 = (2 -1)/(y-3)
Multiply (y-3) times each side of the equation.
Simplify and solve for y.
To find the value of y, we need to use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
We are given the slope of the line, which is 2. Now let's find the y-intercept using one of the given points: (1, 3).
Substituting the values of x and y from the point (1, 3) into the equation, we get:
3 = 2(1) + b
Simplifying, we have:
3 = 2 + b
To isolate b, we subtract 2 from both sides of the equation:
3 - 2 = b
1 = b
Now we have the value of the y-intercept, b, which is 1.
To find the value of y at x = 2, we can substitute the x-value into the equation:
y = 2(2) + 1
Simplifying, we have:
y = 4 + 1
y = 5
Therefore, the value of y when x = 2 is 5.