Question

What is the Y intercept of the line graphed on the grid

Answer 1

5.5

Explanation:

The y-intercept of the line graph shown above is the value of the point where the line cuts the y-axis. The y-intercept of this graph is between 5 and 6. However, we can get an accurate value by calculation. This can be done by generating an equation of the line.

Recall the slope-intercept equation,
`y = mx + b`, where m = slope of the line, b = y-intercept.

To generate the equation of the line, first find slope using the points (-2, 7) and (6, 1):

`slope (m) = (y_2 - y_1)/(x_2 - x_1) = (1 - 7)/(6 -(-2)) = (-6)/(8) = -(3)/(4)`.

Substitute m = ¾ and the coordinates (6, 1) into the slope-intercept equation to find the y-intercept (b):

`y = mx + b`

`1 = -(3)/(4)(6) + b`

`1 = -(18)/(4) + b`

`1 = -4.5 + b + 4.5`

`1 + 4.5 = -4.5 + b + 4.5`

`5.5 = b`

Therefore, b = y-intercept = 5.5.

To generate the equation of the line, plug in the values of m and b, we would have:

y = ¾x + 5.5

The y-intercept of the line of the graph is 5.5.