Question

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

Answer 1

Answer:

5.5

Step-by-step 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):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{6 -(-2)} = \frac{-6}{8} = -\frac{3}{4}$.

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

$y = mx + b$

$1 = -\frac{3}{4}(6) + b$

$1 = -\frac{18}{4} + b$

$1 = -4.5 + b + 4.5$

$1 + 4.5 = -4.5 + b + 4.5$

$5.5 = b$

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.