Find the equation of the line with y-intercept of -11 and slope of −2/7 (2 points)

Question

y = [-11, 11 2/7, 0, 11, -1, 2/7, -11 2/7, 1, -2/7], x + [-11, 11 2/7, 0, 11, -1, 2/7, -11 2/7, 1, -2/7]

Answer 1

The equation of a line can be described by the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is -2/7 and the y-intercept is -11, we can substitute these values into the slope-intercept form to find the equation of the line.

y = (-2/7)x - 11

Therefore, the equation of the line with a y-intercept of -11 and a slope of -2/7 is y = (-2/7)x - 11.

Answer 2

Write an equation of the line that passes through the given points (-4, -2) and (-3, 5)

y = [7, 26, -7, 10, 8, 1, -1, 0, 1, -1, 0, 10, -12] x + [7, 26, -7, 10, 8, 1, -1, 0, 1, -1, 0, 10, -12]

Answer 3

To find the equation of a line that passes through two given points, we can use the point-slope form, which is y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of one of the points and m is the slope of the line.

Given the points (-4, -2) and (-3, 5), we can calculate the slope:

m = (y₂ - y₁) / (x₂ - x₁)
= (5 - (-2)) / (-3 - (-4))
= (5 + 2) / (-3 + 4)
= 7 / 1
= 7

Let's choose the point (-4, -2) to substitute into the point-slope form:

y - (-2) = 7(x - (-4))

Simplifying:

y + 2 = 7(x + 4)

Now we can further simplify and convert the equation into slope-intercept form (y = mx + b) by expanding and rearranging:

y + 2 = 7x + 28
y = 7x + 28 - 2
y = 7x + 26

Therefore, the equation of the line that passes through the points (-4, -2) and (-3, 5) is y = 7x + 26.