Question

Please help. please also look at the 2nd image

Answer 1

The y-intercept for the given relationship is -4. Interpolating between the points (-1, -5) and (1, -3) when x = 0, we estimate that y = -4.

The y-intercept is the point where the graph of a function crosses the y-axis. In the table you provided, when x = 0 (since it's not explicitly given), we can find the corresponding y-value.

Let's interpolate based on the given points:

`\[ x = 0, \quad y = ? \]`

Since there's no specific point given for x = 0, we need to interpolate. If we assume that the relationship is linear between the given points, we can interpolate the value of y when x = 0 using the points -1, -5 and 1, -3 since 0 is exactly in the middle.

Interpolation formula:

`\[ y_{\text{intercept}} = y_1 + ((x - x_1) \cdot (y_2 - y_1))/(x_2 - x_1) \]`

Let's calculate it:

`\[ y_{\text{intercept}} = -5 + ((0 - (-1)) \cdot ((-3) - (-5)))/(1 - (-1)) \]\[ y_{\text{intercept}} = -5 + (1 \cdot 2)/(2) = -5 + 1 = -4 \]`

Therefore, the y-intercept for this relationship is y = -4.