line (-5,-10),(-1,5) — step-by-step solution

The slope between the two points is

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

\frac{5 + 10}{- 1 + 5}

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

5 + 10

15

- 1 + 5

4

⇥

\frac{15}{4}

The line passes through the first point with this slope:

y = \frac{15}{4} \cdot (x + 5) - 10

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

- 10 - \frac{15}{4} \cdot (-5)

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

- \frac{15}{4} \cdot (-5)

\frac{15}{4} \cdot 5

⇥

- 10 + \frac{15}{4} \cdot 5

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

\frac{15}{4} \cdot 5

\frac{15 \cdot 5}{4}

\frac{75}{4}

⇥

- 10 + \frac{75}{4}

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

- 10 + \frac{75}{4}

\frac{4 \cdot (-10) + 75}{4}

⇥

\frac{4 \cdot (-10) + 75}{4}

⇥ⓘ Multiplications are done before additions and subtractions. A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

4 \cdot (-10)

-40

⇥

\frac{- 40 + 75}{4}

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

- 40 + 75

35

⇥

\frac{35}{4}

▶Line:

y = \frac{15 x}{4} + \frac{35}{4}