Question

If (0,4) and (4,0) both lie on 1 find the values of a and b.

a. a = 2, b = 2
b. a = 4, b = 4
c. a = 1, b = 1
d. a = 3, b = 3

Answer 1

To find the values of a and b, we need to determine the equation of the line. Using the given points (0,4) and (4,0), we can find the slope of the line and then substitute one point and the slope to find the y-intercept. The resulting equation is y = -x + 4, so a = -1 and b = 4.

Step-by-step explanation:

The given problem states that the points (0,4) and (4,0) both lie on a line. To find the values of a and b, we need to determine the equation of the line. We can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the given points (0,4) and (4,0) we can find the values of a and b.

Using the formula for finding the slope, m = (y2 - y1) / (x2 - x1), we have m = (0 - 4) / (4 - 0) = -4/4 = -1.

Now that we know the slope is -1, we can substitute one of the points and the slope into the slope-intercept form. Let's use the point (0,4): 4 = -1(0) + b. Solving for b, we get b = 4.

Therefore, the equation of the line is y = -x + 4. So, a = -1 and b = 4.