Question

Write the equation
for this line in
slope-intercept form.

y = ?/?x+ ?

Answer 1

y = 2/3x - 1 (or y = 2/3x + -1 to fit the graphic)

Explanation:

Slope intercept form is written as (y = mx + b) where m is slope and b is the y intercept.

First you need to find the slope, m. We'll use the two points (-3, -3) and (3, 1)

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

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

m = 4/6

m = 2/3

Next we need the y intercept, b. On the graph we can see that is -1 but we can also find it substituting the known slope and one point on the line for our values to solve for b. We'll use (3, 1) as the point.

y = mx + b

1 = 2/3 * 3 + b

simplify 2/3 * 3

1 = 2 + b

subtract 2 from both sides

-1 = b

Now we have all the values we need to plug into our slope intercept equation (m = 2/3, b = -1)

y = mx + b

y = 2/3x - 1

Answer 2

`\sf{y=\displaystyle(2)/(3) x-1`

Solution:

• We are given two points: (3, 1) and (-3, -3).
• We can use these points to find the slope of the line:
• m=
  `\displaystyle(y2-y1)/(x2-x1)`
• 
  `\displaystyle(-3-1)/(-3-3) =(-4)/(-6) =(2)/(3) \longleftarrow\sf{slope}`
• Now, we need to identify the line's y-intercept.
• The y-intercept is the point where the graph touches the y-axis.
• Since the graph touches the y-axis at (0, -1) the y-intercept is equivalent to (0, -1) or -1.

Hope it helps.

Do comment if you have any query.