Question

Here’s a graph of a linear function. Write the equation that describes that function. (Zoom in if blurry)

(Express it in slope-intercept form.)

Answer 1

y=x+1

Explanation:

rise of 1, run of 1, and y-intercept is one

Answer 2

Answer: y = x + 1

Explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the graph,

y2 = 6

y1 = 2

x2 = 5

x1 = 1

Slope,m = (6 - 2)/(5 - 1) = 4/4 = 1

To determine the intercept, we would substitute x = 1, y = 2 and m= 1 into y = mx + c. It becomes

2 = 1 × 1 + c

2 = 1 + c

c = 2 - 1

c = 1

The equation becomes

y = x + 1