Lines t and w are parallel in the xy-plane. The equation of line is 4x + 7y = 14, and line w passes through (-3,9). What is the vaule of the y- intercept of line w?
the actual question on the sat uses the point (-3,8), so I'll use that instead. So first the problem states that the lines are parallell, which means they have the same slope, but diff y-int. using the equation 4x+7y=14, we solve for the equation in y=mx+b form, because currently it is in standard form. Now, we only need the slope, which is -4/7 after rewriting the equation. since they give us the point (-3,8), we will make an equation in y=mx+b form using the slope we just found, and the points given. Now since we know they are parallel lines, the same slope applies, so we now plug in our values to solve for the y intercept, which will be the answer. 8=-4/7(-3)+b is what we get when we plug all in. now, using basic algebra, we solve for b and get the answer:
44/7 or 6.29