Write the standard form of the line that passes through the given points. Include your work in your final answer. Type your answer in the box provided to submit your solution.
(-8, 0) and (1, 5)
To find the equation in standard form of the line passing through the given points, we can use the point-slope form of an equation of a line, which is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope of the line.
First, we need to find the slope of the line. We can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (-8, 0) and (1, 5), we have:
m = (5 - 0) / (1 - (-8))
= 5 / 9
Now we can choose one of the points to substitute into the point-slope form. Let's use the point (-8, 0). Plugging in the values, we get:
y - 0 = (5/9)(x - (-8))
y = (5/9)(x + 8)
Simplifying this equation, we have:
y = (5/9)x + (40/9)
To convert this equation to standard form, we can rearrange the equation to have all the terms on one side:
- (5/9)x + y = (40/9)
Multiplying every term in the equation by 9 to eliminate the fraction, we get:
-5x + 9y = 40
Therefore, the standard form of the line passing through the points (-8, 0) and (1, 5) is -5x + 9y = 40.