Question

What is the equation of the line that passes through the point (3,5) and has a slope of 1?

Answer 1

The equation of a line can be written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

Since the slope is given as 1, we can substitute it into the equation as follows:

y = 1x + b

Now, we need to find the value of b. To do so, we can use the fact that the line passes through the point (3,5).

Substituting the x and y values into the equation, we get:

5 = 1(3) + b

Simplifying this equation, we have:

5 = 3 + b

To isolate b, we subtract 3 from both sides of the equation:

5 - 3 = b

2 = b

Therefore, the value of b is 2.

The final equation of the line passing through the point (3,5) with a slope of 1 is:

y = x + 2.