Answer:
Part a: a) (-1, 14) and b) (-2, 10)
Part of b: Equation of the line: y = 4x + 18
Explanation:
Part a Step 1: Find the equation of the line in slope-intercept form:
The general equation of the slope=intercept form is:
y = mx + b, where
- (x, y) are one point on the line,
- m is the slope,
- and b is the y-intercept.
We can plug in (-3, 6) for (x, y) and 4 form to find b, the y-intercept of the line:
6 = 4(-3) + b
6 = -12 + b
18 = b
Thus, the equation of the line is y = 4x + 18
All the points in a) are in (x, y) form. Thus, we can plug in each x value and see that we get the corresponding y-value to see which points we'd also find on the line:
Checking (-1, 14) for (x, y):
14 = 4(-1) + 18
14 = -4 + 18
14 = 14
Thus, (-1, 14) lies on the line. Therefore, a) is one of our answers.
Checking (-2, 10) for (x, y):
10 = 4(-2) + 18
10 = -8 + 18
10 = 10
Thus, (-2, 10) lies on the line. Thus, b) is also one of our answers.
Checking (0, 0) for (x, y):
The only line that passes through (0, 0) is y = x as (0, 0) is the origin and only y = x passes through the origin. Thus, (0, 0) is not one of our answers.
Checking (1, 14) for (x, y):
A linear function has a constant slope and will never pass through the same y-coordinate twice. Furthermore, for any function to be classified a function, every x-coordinate can only be paired to one y-coordinate. Thus, since we've already determined that (-1, 14) lies on the line, we know that (1, 14) can't and doesn't lie on the line.
Checking (2, 10) for (x, y):
Similarly, since we already found that (-2, 10) lies on the line, we know that (2, 10) also can't and doesn't lie on the line.
Part b:
We found in part a that the equation of the line is y = 4x + 18