Question

Find the equation of the straight line which passes through the point (3,1) and with gradient 3. Hence please find the coordinates of the point of intersection of the line with another line with equation y=x.

Answer 1

The equation of the straight line is y = 3x - 8. The coordinates of the point of intersection with the line y = x are (4,4).

Step-by-step explanation:

The equation of a straight line can be expressed in the form y = mx + b, where m is the gradient and b is the y-intercept. Given that the line passes through the point (3,1) and has a gradient of 3, we can substitute those values into the equation to find the value of b. Thus, the equation of the line is y = 3x - 8.

To find the coordinates of the point of intersection with the line y = x, we can set the two equations equal to each other and solve for x. This gives us the equation x = 3x - 8. Solving this equation, we find that x = 4. Substituting this value of x into either equation, we find that y = 4. Therefore, the coordinates of the point of intersection are (4,4).