Question

Find an equation of the line that passes through the points (1,2) and (2,3).

Answer 1

Answer:

y=x+1

Step-by-step explanation:

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

m=(3-2)/(2-1)

m=1/1

m=1

y-y1=m(x-x1)

y-2=1(x-1)

y-2=x-1

y=x-1+2

y=x+1

Answer 2

Slope-intercept form:  y = mx + b

[m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y) or the point where the line crosses through the y-axis]

To find the slope(m), use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$         And plug in the two points

(1, 2) = (x₁, y₁)

(2, 3) = (x₂, y₂)

[lines go from left to right, so the point furthest to the left is the 1st point]

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{3-2}{2-1}$

$m=\frac{1}{1}$

m = 1     Now that you found the slope, plug it into the equation

y = mx + b

y = 1x + b    or   y = x + b        To find b, plug in one of the points into the equation (doesn't matter which point, I will use (1, 2))

2 = (1) + b     Subtract 1 on both sides to get b by itself

2 - 1 = 1 - 1 + b

1 = b      

y = x + 1