There is no significant change in the rate of improvement of black high school graduation rates until the late 80's, when improvements slow down. That is, the Civil Rights Act obviously didn't help improve black graduation rates.
I think you misunderstand what the word "evidence" means. Evidence is data that either agrees or disagrees with the predictions of a theory.
Let's say you observe that high school graduation rates are much higher for white students than black ones. That has been true for years, and there's no sign of the gap shrinking. You're pretty sure it's caused by discrimination, so you pass a law outlawing discrimination based on race.
You did that based on a theory that says anti-discrimination laws work. That theory leads to a prediction: once the law is passed, the gap should start to shrink. So you wait a while and sure enough, it does. The data agrees with the prediction of the theory, so it is evidence supporting the theory.
Of course, one piece of evidence isn't conclusive. The real world is a complicated place. Maybe the gap shrank for some other reason. Maybe it would have happened even without the law. So you need to look at lots of data. You can look at other measures of academic success, like earning college degrees and scores on standardized tests. The theory predicts you'll see improvement on multiple measures, not just one. (You do.) Even better, look at other kinds of discrimination. Don't just ban discrimination based on race, but also gender, age, disability status, etc. That gives you several different groups to look at. The theory predicts you'll see shrinking achievement gaps for all of them. (You do.)
This adds up to a lot of evidence, all supporting the theory. That still isn't conclusive. You can always try to argue some other factor might have caused the changes. But still, all the data matches the predictions of the theory. There's a lot of evidence supporting the theory, and very little contradicting it.
Hopefully it's now obvious what's wrong with the argument you tried to make? You were trying to evaluate a theory by comparing it to predictions it didn't make! Graduation rates are constantly changing based on lots of factors other than discrimination: economic changes, social trends like urbanization, changing levels of government spending on education, etc. You can't just make a linear extrapolation from the last five years and assume they'll continue on that same line indefinitely. No sensible theory makes that prediction.
Suppose I say to you, "20 years from now, there will be less discrimination than there is today. Based on that, tell me what the high school graduation rate will be in 20 years." You can't answer that. You don't have enough information. The answer depends on lots of other things that will happen over the next 20 years. Just knowing what will happen with discrimination isn't enough to make a prediction.
But you can still predict that the gap should shrink. Whatever happens to the economy or government spending, the people who previously faced discrimination should improve relative to the ones who didn't. Discrimination means treating people differently. Unequal treatment leads to unequal outcomes. If the treatment becomes more uniform, the outcomes should too. You can only evaluate a theory based on the predictions it makes, not the ones it doesn't make.
And, again, even if the Civil Rights Act had helped improve black graduation rates, it would have done so through the elimination of government racial discrimination, not any laws related to private businesses, since private businesses have little influence on high school graduation rates.
You're the one who cited that graph, not me! In this whole conversation, you have only given two links to anything resembling concrete data on the effects of anti-discrimination laws. One of them was to that graph, which you're now saying is irrelevant to the discussion. So why did you cite it in the first place???