Question

What is the equation of a line that passes through the points (0,4) and (3,8)?

Answer 1

y = 4/3x + 4

Explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (0,4) and (3,8)

We see the y increase by 4 and the x increase by 3, so the slope is

m = 4/3

Y-intercept is located at (0,4)

So, the equation is y = 4/3x + 4

Answer 2

The slope of the line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, 4) and (x2, y2) = (3, 8)

slope = (8 - 4) / (3 - 0) = 4/3

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the given points. Choosing (0, 4) as the point, we get:

y - 4 = (4/3)(x - 0)

Simplifying:

y - 4 = (4/3)x

y = 4/3 x + 4

Therefore, the equation of the line is y = 4/3 x + 4.