Answer:
[tex]y= \frac{1}{5}x + 1[/tex]
Step-by-step explanation:
Given points (0,1) and (5,2):
Let (x1, y1) = (0,1)
(x2, y2) = (5,2)
Use the follwing slope formula to calculate the slope of the line:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Plug in the values for (x1, y1) and (x2, y2):
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{2 - 1}{5 - 0} = \frac{1}{5}[/tex]
Therefore, the slope of the line is [tex]\frac{1}{5}[/tex] .
Next, we must determine the y-intercept, which is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is the value of y when x = 0.
Therefore, using the slope-intercept form, y = mx + b, and one of the points, (5, 2):
Let y = 2, x = 5, and m = [tex]\frac{1}{5}[/tex]
y = mx + b
2 = [tex]\frac{1}{5}(5)[/tex] + b
2 = 1 + b
Subtract 1 from both sides of the equation:
2 - 1 = 1 + b - 1
b = 1
The y-intercept of the line is (0, 1), or b = 1.
Therefore, the equation of the line is:
[tex]y= \frac{1}{5}x + 1[/tex]
