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

1 answer

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 slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

Substitute the values of the points into the formula:

slope = (5 - 1) / (3 - 1)
slope = 4 / 2
slope = 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 and one of the points into the formula:

y - 1 = 2(x - 1)

Distribute the 2:

y - 1 = 2x - 2

Add 1 to both sides:

y = 2x - 1

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