Graphs of linear equations and functions: foundations

Question

Google Classroom
Problem
A line in the xy-plane passes through the points (0, 1) and (1, 5).





















A line in the xy-plane passes through the points (0, 1) and (1, 5).
What is the y-intercept of the line in the xy-plane?

Answer 1

To find the y-intercept of the line, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point that the line passes through.

First, we find the slope of the line using the two given points:

m = (y2 - y1) / (x2 - x1)
m = (5 - 1) / (1 - 0)
m = 4

Now, we can use the slope and one of the points to find the equation of the line:

y - 1 = 4(x - 0)
y - 1 = 4x
y = 4x + 1

Since the y-intercept is the value of y when x is 0, we can substitute x = 0 into the equation:

y = 4(0) + 1
y = 1

Therefore, the y-intercept of the line in the xy-plane is 1.