Question

Find the equation of the line that passes through the following two points:
(5, 7) and (1, 10)

Answer 1

Answer: y=-3/4x+43/4

Step-by-step explanation:

y = mx+b

m is the slope, and

b is the y-intercept

m= y2-y1 /  x2-x1

m= 10-7/ 1-5

m=-3/4

Answer 2

Answer: y = $-\frac{3}{4}$x + 10 $\frac{3}{4}$

Step-by-step explanation:

       If we know the two points, we can find the slope and write a point-slope equation.

       Slope

$\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{10-7}{1-5} =\frac{3}{-4} =\frac{-3}{4}$

       Point-slope equation

y - $y_1$ = m(x - $x_1$)

y - 7 = $-\frac{3}{4}$(x - 5)

y - 7 = $-\frac{3}{4}$x + 3 $\frac{3}{4}$

y = $-\frac{3}{4}$x + 10 $\frac{3}{4}$

       Slope-intercept form equation

y = $-\frac{3}{4}$x + 10 $\frac{3}{4}$