Question

What is an equation of the line that passes through the points (-1,-5) and (1, 3)?

Answer 1

y = 4x + 1

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First calculate the slope using the formula:

• m = (y₂-y₁)/(x₂-x₁),

where (x₁,y₁) = (-1,-5) and (x₂,y₂) = (1,3).

This gives us a slope of:

• m = (3-(-5))/(1-(-1)) = 8/2 = 4

Next, we can use the point-slope form of a linear equation:

• y - y₁ = m(x - x₁),

where (x₁,y₁) is one of the given points and m is the slope.

Let's use the point (-1,-5). Substituting the values into the equation, we get:

• y - (-5) = 4(x - (-1))
• y + 5 = 4(x + 1)

Finally, we can write the equation in slope-intercept form:

• y = mx + b,

where m is the slope and b is the y-intercept.

Rearranging the equation, we have:

• y = 4x + (5 - 4)
• y = 4x + 1

Therefore, the equation of the line is y = 4x + 1.