To find the gradient and the $y$-intercept of the line, we need to rewrite the equation in the slope-intercept form: $y = mx + c$, where $m$ is the gradient and $c$ is the $y$-intercept.

The given equation is:

$y - 7 = 6x + 11$

Step 1: Rearrange for $y$

Add 7 to both sides:

$y = 6x + 11 + 7$

Simplify:

$y = 6x + 18$

Step 2: Identify the gradient and $y$-intercept

• Gradient ($m$): The coefficient of $x$ is $6$.
• $y$-intercept ($c$): The constant term is $18$.

Final Answer:

• Gradient: $6$
• $y$-intercept: $18$

Let me know if you'd like further clarification!

Here are some follow-up questions to expand on this topic:

1. What is the significance of the gradient in a linear equation?
2. How does changing the $y$-intercept affect the graph of the line?
3. What would happen to the line if the gradient were negative?
4. How can we find the $x$-intercept of this line?
5. What is the equation of a line parallel to this one but passing through a different point?

Tip: Always ensure the equation is in slope-intercept form for easier interpretation of the line’s characteristics.