line (2,3),(-1,5) — step-by-step solution

The slope between the two points is

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

\frac{5 - 3}{- 1 - 2}

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

5 - 3

2

- 1 - 2

-3

⇥

\frac{2}{-3}

⇥ⓘ The sign of a fraction goes in front of the bar, whether it comes from the numerator or the denominator:

\frac{2}{-3}

- \frac{2}{3}

⇥

- \frac{2}{3}

The line passes through the first point with this slope:

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

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

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

⇥ⓘ Two minus signs cancel out, the product of two negative numbers is positive:

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

\frac{2}{3} \cdot 2

⇥

3 + \frac{2}{3} \cdot 2

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

\frac{2}{3} \cdot 2

\frac{2 \cdot 2}{3}

\frac{4}{3}

⇥

3 + \frac{4}{3}

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

3 + \frac{4}{3}

\frac{3 \cdot 3 + 4}{3}

⇥

\frac{3 \cdot 3 + 4}{3}

⇥ⓘ Multiplications are done before additions and subtractions:

3 \cdot 3

9

⇥

\frac{9 + 4}{3}

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

9 + 4

13

⇥

\frac{13}{3}

▶Line:

y = - \frac{2 x}{3} + \frac{13}{3}