Bot GPT 4-o mini To find the correct linear equation representing the nonproportional linear relationship shown in the table, we can analyze the given points.
The table appears to represent the following points:
- (-5, 0)
- (0, 5)
- (2, 7)
First, we can determine the slope (m) of the line that passes through these points using two of the points, say (0, 5) and (2, 7):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 5}{2 - 0} = \frac{2}{2} = 1 \]
Now, we will use the point-slope form of the linear equation y = mx + b to find the y-intercept (b). Since we already found the slope (m = 1), we can substitute one of the points, for example, (0, 5):
\[ y = 1(x) + b \] \[ 5 = 1(0) + b \] \[ b = 5 \]
So, the equation of the line in slope-intercept form is:
\[ y = 1x + 5 \]
This can also be written simply as:
\[ y = x + 5 \]
Now, let’s check if any of the given options match this equation.
The correct option from the provided responses is:
y = x + 5
1 answer