Given a line with a y-intercept of -5 and an x-intercept of 6, what is the equation of the line?

To determine the equation of a line given its y-intercept and x-intercept, you can use the slope-intercept form of a linear equation, which is ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.

The y-intercept is the point where the line crosses the y-axis, which is given as -5. Therefore, the value of ( b ) in the equation will be -5.

The x-intercept is the point where the line crosses the x-axis, given as 6. This means that when ( y = 0 ), ( x = 6 ). By substituting these values into the equation, you can find the slope (( m )).

To find the slope, you can use the coordinates of the two intercepts: the y-intercept ( (0, -5) ) and the x-intercept ( (6, 0) ). The slope ( m ) is calculated as follows:

[

m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-5)}{6 - 0} = \