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

y = mx + b

5 = 3(1) + b
2 = b
and m =3

y=3x + 2

since you are given a point and a slope, start with the point-slope form:

y-5 = 3(x-1)

Now just rearrange things to get what you need.

To find the equation of a line in slope-intercept form (y = mx + b), you need to determine the values of the slope (m) and the y-intercept (b).

In this case, you are given the slope (m = 3) and a point that the line passes through (1, 5). To proceed, you can follow these steps:

Step 1: Start with the point-slope form of the equation: y - y₁ = m(x - x₁).
- Substitute the values of the given point (x₁, y₁) = (1, 5) and the slope (m = 3).
- This gives you: y - 5 = 3(x - 1).

Step 2: Simplify the equation to slope-intercept form (y = mx + b) by solving for y.
- Distribute 3 across the terms in the parentheses: y - 5 = 3x - 3.
- Combine like terms: y = 3x - 3 + 5.
- Simplify further: y = 3x + 2.

So, the equation of the line that passes through the point (1, 5) and has a slope of 3 is y = 3x +2.