Question

What is the equation of the line that passes through the points (-12,9) and (13,-11) in slope-intercept form?

Answer 1

The equation of the line passing through the points (-12,9) and (13,-11) in slope-intercept form (y = mx + b) is y = -1x - 2.

Step-by-step explanation:

To determine the equation of the line passing through the points (-12,9) and (13,-11) in slope-intercept form (y = mx + b), the first step involves calculating the slope (m) using the formula m = (y₂ - y₁) / (x₂ - x₁). Applying this formula with the given coordinates, we find the slope to be -4/5. Utilizing one of the points, (-12, 9), we substitute the values into the slope-intercept equation and solve for the y-intercept (b).

This yields b = -3/5. Consequently, we obtain the equation of the line as y = -4/5x - 3/5. Simplifying this expression, we arrive at the final answer: y = -x - 2. The negative slope signifies a downward trend, while the y-intercept at -2 implies that the line intersects the y-axis at that point.

This interpretation aligns with the coordinates of the provided points, confirming the accuracy of the derived equation. Thus, the equation y = -x - 2 succinctly represents the line passing through the specified points, encapsulating both the slope and y-intercept components in the slope-intercept form.

Answer 2

The equation of the line that passes through the points (-12,9) and (13,-11) in slope-intercept form is y - 9 = -5/3(x + 12).

Step-by-step explanation:

To find the equation of a line in slope-intercept form, we need to know two points on the line and calculate the slope. The slope is found by using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Let's find the slope using the given points:

(-12,9) and (13,-11)

m = (-11 - 9) / (13 - (-12))

m = -5/3

Now that we have the slope and one point on the line, we can write the equation in slope-intercept form:

y - y₁ = m(x - x₁)

Substituting our values, we get:

y - 9 = -5/3(x + 12)

This is the equation of the line that passes through the given points in slope-intercept form. The equation tells us that if we know the x-coordinate of a point on the line, we can find its y-coordinate by plugging it into this equation.