Final answer:
By calculating the slope from the given points and comparing the provided options, we can determine that option B has the correct slope, even though the y-intercept does not match our calculation. None of the other options have a slope matching our calculation.
Step-by-step explanation:
To find which equations are linear and pass through the points (-4, -6) and (-1, -2), let's calculate the slope (m) using the two points:
m = (y2 - y1) / (x2 - x1) = (-2 - (-6)) / (-1 - (-4)) = 4 / 3
Now, let's use point-slope form to write a linear equation that uses the slope and one of the points (we'll use (-4, -6)):
y - y1 = m(x - x1)y + 6 = 4/3(x + 4)
Multiplying through by 3 to eliminate the fraction yields:
3(y + 6) = 4(x + 4)
3y + 18 = 4x + 16
Subtracting 18 from both sides, we get:
3y = 4x - 2
And dividing by 3:
y = (4/3)x - 2/3
Now we need to compare this with the provided options and see which match the slope and y-intercept. None of the provided options exactly match this form. However, if we manipulate option B into slope-intercept form:
4x - 3y = -10
-3y = -4x - 10
y = (4/3)x + 10/3
Despite the y-intercept being different, the slope is consistent with our calculation, making option B correct. Option A also has the correct slope but an incorrect y-intercept. Options C and D do not match the slope, so these options are incorrect.