The Linear equation y=6x-5 graphs as a horizontal/vertical/diagonal line ( choose the correct label and type it below)
diagonal
To determine whether the linear equation y = 6x - 5 graphs as a horizontal, vertical, or diagonal line, we can analyze the equation's form.
In general, a linear equation can be written in the form y = mx + b, where m represents the slope and b represents the y-intercept.
In the given equation y = 6x - 5, the coefficient in front of x is 6. This value represents the slope of the line.
Since the slope is non-zero (6 ≠ 0), the line will not be a horizontal line.
If the equation had been of the form y = mx + b, and the constant term (the number not multiplied by x) had been zero, like y = 6x + 0, then it would be a horizontal line.
Since the equation does not contain a constant term, the y-intercept is -5. This implies that the line passes through the point (0, -5).
Knowing that the line has a non-zero slope and passes through the point (0, -5), we can conclude that it cannot be a vertical line either.
Therefore, the line represented by y = 6x - 5 is a diagonal line.