Question

Write the equation of the linear function that passes through the points ( 1, 1) and ( 3 , 5 ) . Help Video, if needed.(1 point)

Answer 1

To find the equation of the linear function that passes through the points (1,1) and (3,5), we first need to find the slope of the line.

The formula to find the slope of a line passing through two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)

Using the points (1,1) and (3,5):
m = (5 - 1) / (3 - 1)
m = 4 / 2
m = 2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)

Substitute the slope (m = 2) and one of the points (1,1) into the equation:
y - 1 = 2(x - 1)

Expand the equation:
y - 1 = 2x - 2

Add 1 to both sides to solve for y:
y = 2x - 1

Thus, the equation of the linear function that passes through the points (1,1) and (3,5) is y = 2x - 1.