Question

Which is an equation in slope intercept form of the line that passes through (1, 3) and (2, 4)?​

Answer 1

Answer:

y = x + 2

Step-by-step explanation:

The slope-intercept equation is:

y = mx + b

First, you should use the point-slope formula to find the slope. Plug in the "x" and "y" values given from the points:

Point 1: (1,3)        Point 2: (2,4)

y₁ - y₂ = m(x₁ - x₂)               <--- Point-slope formula

(3 - 4) = m(1 - 2)                  <--- Plug in "x" and "y" values from points

-1 = -m                                <--- Simplify inside parentheses

1 = m                                  <--- Divide both sides by -1

Finally, use one of the points to solve for the y-intercept (b):

Point 1: (1,3)           m = 1

y = mx + b                       <--- Slope-intercept formula

3 = 1(1) + b                       <--- Plug in values from point and slope (m)

3 = 1 + b                          <--- Multiply slope and "x" value

2 = b                               <--- Subtract 1 from both sides

Since the slope = 1, it does not need to be included in the final formula. The final answer is:

y = x + 2