Question

A line crosses through the point (3,10) and another point can be found on the line by going right 2 and down 7. find slope and y intercept

Answer 1

Answer:

y =  $\frac{-7x}{2}+\frac{41}{2}$

Step-by-step explanation:

We are given the point (3, 10).

The second point is 2 on the x-axis and -7 on the y-axis. So our second point is: (3 + 2, 10 - 7) which is (5, 3).

Our formula for slope is m = $\frac{rise}{run}$ = $\frac{y2-y1}{x2-x1}$

So, our equation would be $\frac{3-10}{5-3}$ = $\frac{-7}{2}$

Using the standard formula of a line, y = mx + b, we can substitute for the slope, m.

y = $\frac{-7x}{2}$ + b

Now, we can substitute a point on the line to determine the y-intercept:

Using the point (3, 10),

10 = $\frac{-7(3)}{2}$ + b

b = 10 + $\frac{21}{2}$

b = $\frac{41}{2}$

So our full equation is: y =  $\frac{-7x}{2}+\frac{41}{2}$