Write an equation in slope-intercept form of the line satisfying the given conditions.
Through (3, -1), parallel to 8 x - 7 y = -11
To write the equation of the line in slope-intercept form, we first need to find the slope of the given line. We can rewrite the given equation in slope-intercept form (y = mx + b) by isolating y:
8x - 7y = -11
-7y = -8x - 11
y = (8/7)x + 11/7
Now that we have the slope of the given line, which is 8/7, we can write the equation of the line that is parallel to it and passes through the point (3, -1). We can use the point-slope form of the equation:
y - y1 = m(x - x1)
Replacing (x1, y1) = (3, -1) and m = 8/7, we get:
y - (-1) = (8/7)(x - 3)
y + 1 = (8/7)x - 24/7
Now, let's isolate y to write the equation in slope-intercept form:
y = (8/7)x - 24/7 - 1
y = (8/7)x - 24/7 - 7/7
y = (8/7)x - 24/7 - 7/7
y = (8/7)x - 31/7
Therefore, the equation of the line parallel to 8x - 7y = -11 and passing through (3, -1) is y = (8/7)x - 31/7 in slope-intercept form.