Question

Write an equation in slope-intercept form of the line that passes through $\left(1,\ 4\right)$ and $\left(3,\ 10\right)$ .

Answer 1

The equation in slope-intercept form for the line passing through (1, 4) and (3, 10) is y = 3x + 1.

Step-by-step explanation:

The equation in slope-intercept form to describe the line that passes through the points (1, 4) and (3, 10) will take the form of y = mx + b, where m is the slope and b is the y-intercept. First, calculate the slope by finding the change in y divided by the change in x (rise over run).

m = (10 - 4) / (3 - 1)

= 6 / 2 = 3

Now that we have the slope, let's use one of the given points to find the y-intercept, b. We'll use the point (1, 4).

4 = 3(1) + b

b = 4 - 3 = 1

Finally, the equation for the line is y = 3x + 1.