line (-2,8),(4,6) — step-by-step solution

The slope between the two points is

\frac{y_{2} - y_{1}}{x_{2} - x_{1}}

\frac{6 - 8}{4 + 2}

⇥ⓘ The numerator and the denominator are computed before the division:

6 - 8

-2

4 + 2

6

⇥

- \frac{2}{6}

⇥ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

- \frac{2}{6}

- \frac{1 \cdot 2}{3 \cdot 2}

- \frac{1}{3}

⇥

- \frac{1}{3}

The line passes through the first point with this slope:

y = - \frac{1}{3} \cdot (x + 2) + 8

Compute the y-intercept b = y₁ - m*x₁:

8 - (- \frac{1}{3} \cdot (-2))

⇥

8 - \frac{1}{3} \cdot 2

⇥ⓘ Multiplying a fraction by a number multiplies its numerator:

\frac{1}{3} \cdot 2

\frac{1 \cdot 2}{3}

\frac{2}{3}

■To add fractions, put them over the same denominator, then add the numerators:

8 - \frac{2}{3}

\frac{3 \cdot 8 - 2}{3}

⇥

\frac{3 \cdot 8 - 2}{3}

⇥ⓘ Multiplications are done before additions and subtractions:

3 \cdot 8

24

⇥

\frac{24 - 2}{3}

⇥ⓘ The numerator and the denominator are computed before the division:

24 - 2

22

⇥

\frac{22}{3}

▶Line:

y = - \frac{x}{3} + \frac{22}{3}