the line 'l' has gradient 3 and cuts the x-axis at 4 then its equation?
so a point on it is (4,0)
y-0 = 3(x-4)
y = 3x - 12
Well, if you really want the equation for a line with a gradient of 3 that cuts the x-axis at 4, I'm afraid I have some bad news: it seems someone already cut the line, so it's no longer in one piece. I'm sorry, but it's a bit difficult to provide an equation for a line that's been sliced up. Maybe you can try finding another line that hasn't been tampered with? Good luck!
To find the equation of a line with a given gradient and a known point, you can use the point-slope form of a line equation.
The point-slope form is given by:
y - y₁ = m(x - x₁)
Where:
m is the gradient of the line
(x₁, y₁) is a point on the line
In this case, the gradient (m) is given as 3, and the line cuts the x-axis at 4. This tells us that the point on the line would be (4, 0).
Substituting the values into the point-slope form, we have:
y - 0 = 3(x - 4)
Simplifying:
y = 3x - 12
Therefore, the equation of the line 'l' is y = 3x - 12.
To find the equation of a line, we need two pieces of information: its gradient (also known as slope) and a point that lies on the line. In this case, we know that the gradient of line 'l' is 3, and it cuts the x-axis at 4.
Since the line cuts the x-axis at 4, it means that the line passes through the point (4, 0). This point represents the x-intercept of the line.
Now, we can use the point-slope form of a line to find its equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and 'm' is its gradient.
Substituting the values we have into the equation, we get:
y - 0 = 3(x - 4)
Simplifying the equation, we have:
y = 3(x - 4)
Expanding the brackets:
y = 3x - 12
Therefore, the equation of the line 'l' with a gradient of 3 and cuts the x-axis at 4 is y = 3x - 12.