The given equation of the straight line is:

$y = 6x + 3$

This equation is in the slope-intercept form of a straight line, which is:

$y = mx + c$

Where:

• $m$ is the slope (gradient) of the line.
• $c$ is the y-intercept, the value of $y$ when $x = 0$.

Step 1: Identify the gradient

From the equation $y = 6x + 3$, we can see that:

• The gradient (slope) $m = 6$.

Step 2: Identify the y-intercept

The y-intercept $c = 3$, which is the value of $y$ when $x = 0$.

Final Answer:

• Gradient (m) = 6
• Y-intercept (c) = 3

Would you like more details on the process, or do you have any further questions?

Related questions:

1. How can we derive the slope-intercept form of a straight line from two points on the line?
2. How do we determine the gradient of a line given two points?
3. What is the geometric interpretation of the gradient of a line?
4. How can we plot the straight line $y = 6x + 3$?
5. What is the relationship between the slope of a line and the angle it makes with the x-axis?

Tip: The slope of a line represents how steep the line is, with a larger absolute value of the gradient indicating a steeper line.