Question

A straight line l has gradient 2 and passes through the point (0,3) write the equation for l

Answer 1

As we know that a straight line is represented by its equation, which is in the form of y = mx + c where m is the gradient and c is the y-intercept of the line.

Here, the gradient of the line l is given as 2 and the point (0,3) lies on the line l. We can use the point-slope form of a line to write the equation of line l.

The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1,y1) is a point on the line and m is the gradient of the line.

Using the given information, we can substitute the values of m, x1 and y1 in the equation:

y - 3 = 2(x - 0)

Simplifying the equation:

y - 3 = 2x

Adding 3 to both sides of the equation:

y = 2x + 3

Therefore, the equation for line l is y = 2x + 3.

Answer 2

The equation for a straight line in slope-intercept form is y = mx + b, where m is the gradient (slope) of the line and b is the y-intercept (the point where the line crosses the y-axis).

We are given that the gradient of the line is 2, so we can substitute m = 2 into the equation:

y = 2x + b

We are also given that the line passes through the point (0,3), which means that when x = 0, y = 3. We can substitute these values into the equation and solve for b:

3 = 2(0) + b

b = 3

Now we know that the y-intercept is 3, so we can write the equation of the line:

y = 2x + 3