Question

Write the equation of the line shown in the graph above in slope-intercept form

Answer 1

Answer: y= -2/3x+1


Step 1: Write slope-intercept form equation

To start answering this question, it helps to write out the example equation for slope-intercept form. Let’s do this now.

y=mx+b

Keep in mine that the y represents the answer, the m represents the slope, the x represents the variable, and the b represents the y-intercept.

Step 2: Determine the y-intercept

I find that it is easiest to determine the y-intercept first. This is the b in the equation. The y-intercept can be find by looking at the y-axis, and seeing where the line intersects with the axis. In this case, it seems to be at 1. Let’s substitute this into our equation now.

y=mx+b
y=mx+1

Step 3: Determine slope

For the final thing that we need to fill in, we need to find the slope. The slope is the m in the equation, and can be found by the formula of rise/run. Choose any two points, and see how far they are from each other up and down (rise), as well as left and right (run).
For the sake of this problem, we will work with (0,1) and (-3,3). There is a difference in the rise of 2 and in the run of 3. This makes the rise/ run be 2/3. Let’s substitute this now.

y=mx+1
y= 2/3x+1

The slope will also need to be negative since the line on the graph descends. Let’s change this to a negative now.

y= -2/3x+1


This is your answer. Hope this helps! Comment below for more questions.

Answer 2

Y = mx + c
y= -2/3x + 1
1= c