Final answer:
The equation of the linear function that has the same slope as x+4y=8 and goes through the point (-12, 5) is y = -1/4x + 2.
Step-by-step explanation:
To find the equation of a linear function that has the same slope as x+4y=8 and goes through the point (-12, 5), we first need to determine the slope of the given line. By rearranging the equation into slope-intercept form, we isolate y:
4y = -x + 8
y = -⅔x + 2
So, the slope of the line is -1/4. According to the slope and the algebra of straight lines, the slope is the same all along a straight line. Now we use the point-slope form to find the equation of our line:
y - y₁ = m(x - x₁)
Substituting the slope m and the point (-12, 5):
y - 5 = -1/4(x - (-12))
y - 5 = -1/4x - 3
Finally, we convert this to slope-intercept form, y = mx + b:
y = -⅔x + 2
Therefore, the equation of the line in slope-intercept form that has the same slope as the given line and passes through the point (-12, 5) is:
y = -1/4x + 2